[SOLVED] Is there a true singularity in nature?

[the softrat]

I am well aware that a number of physical models contain or predict
singularities. My question is: Is there any experimental evidence that
any singularity actually exists or are they all artifacts of the
models?

Lest someone jump right in with the singularity at the center of a
black hole, let me say that, although the various solutions of
Einstein's Equation have provided much useful guidance in
understanding the structure of the universe, as far as I know, the
center of a star or BH is outside of the range (or is it domain) of
applicability of the various solutions because they presume a non-zero
stress-energy tensor. In point of fact, we do not know what is in
there, we just know about the effects at and/or outside of the event
horizon.

It is my belief that there are no singularities in nature. I am
looking for evidence that I am wrong.

Note that renormalization in QED 'takes care of' the singularities,
i.e. they are not really there, just in an incomplete model. I suspect
that a comprehensive theory of quantum gravity may exhibit similar
behavior. Meanwhile, our ingenuity in constructing mathematical models
is less ingenious than Reality itself.

For your kind consideration,

George D. Freeman IV, aka

the softrat
Sometimes I get so tired of the taste of my own toes.
mailto:softrat@pobox.com
--
"Some students drink at the fountain of knowledge, some students
just gargle!" -- Navjot Singh Siddu

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Uncle Al]

the softrat wrote:
>
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?
>
> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor. In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.
>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.
>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
> For your kind consideration,

Cover a sphere with hair normal to its surface. No problem. Add a
new rule - no hair may emerge normal to the surface. You now have two
singularities. Compare with electric and magnetic fields.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[J. J. Lodder]

the softrat <softrat@pobox.com> wrote:

> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

Experimental evidence is irrelevant for your question:
it is in principle impossible to decide on basis of experiments
whether or not a singularity 'really' is a 'true' singularity.
Singularities are idealizations, and real experiments can't be ideal.

Your question is meaningless,

Jan

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Igor Khavkine]

On 2005-09-12, the softrat <softrat@pobox.com> wrote:
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists or are they all artifacts of the
> models?

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

It is also the belief of most physicists. It is generally believed that
anything that can be measured will have a finite value. This belief is
quite reasnable, since only finite measurements have ever been
recorded.

In general, a singularity (which is not spurious, and is in principle
measurable) indicates a failure of the theory in a given context. A more
general theory must be invoked to explain the results of measurements
made in this context (if such are possible).

One example is the singularity in the Newtonian gravitational field
of the Earth. From far away, one can extrapolate to a 1/r^2 divergence,
where r is the distance from Earth's center. However, this divergence is
not there when we get close enough since Earth is of a finite size. In
other words, this divergence tells us that the point mass approximation
fails when we get close enough.

The trouble is that we have some theories that predict singularities
which we can neither measure, nor do we really have a more general
theory that can act as a replacement and predict finite results in the
would-be singular regimes.

Igor

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Kwok Man Hui]

On Mon, 12 Sep 2005, the softrat wrote:

>
> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

So far, there is no direct empirical evidence of observing blackhole
singularity.
However, having the mathmetical prediction of blackhole singularity might
be able to explain some cosmological phenomenon that can't be explained by
other models. For example, billion of light year jet beam coming out of
some discs in space. I think some folks here can explain this much better
than I do. I think classication of singularities in algebraic geometry is
a beautiful theory. I think if there is anything like "quantum
singularity", it will be a beautiful theory.

>
> Note that renormalization in QED 'takes care of' the singularities,
> i.e. they are not really there, just in an incomplete model. I suspect
> that a comprehensive theory of quantum gravity may exhibit similar
> behavior. Meanwhile, our ingenuity in constructing mathematical models
> is less ingenious than Reality itself.
>
I remember vaguely one of the founders of Yang-Mills gauge field theory
said it would be Nature's mistake if it does not take such a beautiful
theory seriously before any experimental confirmation of
electroweak theory. I don't have my books in hands, otherwise I
could have cited you more stories about how mathematical concepts
and great physical theories are parallel developed. Sometime,
great mathematical elegance deserves a glance of Nature. Be open minded.
History has told us numerous times that it would be a mistake if some
beautiful mathematical theories cannot be linked to some physical
concepts.

Charles Hui

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Nick Maclaren]

In article <Pine.LNX.4.62.0509122333310.10789@lab47.ma.utexas. edu>,
Kwok Man Hui <kmhui@math.utexas.edu> writes:
|> On Mon, 12 Sep 2005, the softrat wrote:
|>
|> > It is my belief that there are no singularities in nature. I am
|> > looking for evidence that I am wrong.
|>
|> So far, there is no direct empirical evidence of observing blackhole
|> singularity.
|> However, having the mathmetical prediction of blackhole singularity might
|> be able to explain some cosmological phenomenon that can't be explained by
|> other models. For example, billion of light year jet beam coming out of
|> some discs in space. ...

Hmm. The assumption that they can't be explained by other models
is a pretty extreme one. There is certainly evidence of a very
deep gravitational hole, but that is a far cry from a singularity.

Can anyone here explain to a layman why those observations
necessarily imply a singularity? My brief inspection of papers
indicates that the strongest that can be claimed is that they are
compatible with the existence of a singularity, and that general
relativity predicted that some such phenomena would occur.

|> I think classication of singularities in algebraic geometry is
|> a beautiful theory.

Well, perhaps, but the classification of ones in numerical analysis
assuredly isn't :-)


Regards,
Nick Maclaren.

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[Ian Taylor]

In elastohydrodynamic lubrication, the pressure distribution in the
lubricated contact exhibits a "pressure spike" at the outlet of the
contact. This situation is modelled iteratively by solving the
combination of the Reynolds' equation (for fluid flow assuming the
lubrication approximation) and the elastic deformation equations for
the bounding surfaces. I should add this is quite a complex numerical
analysis problem. The "pressure spike" has also been measured
experimentally. I have always wondered if this is a true singularity
(in the modelled solution, not the experiment !) since when you model
the system on a finer grid you tend to find a sharper "spike".
Quite apart from this example, which is probably completely unfamiliar
to many on this forum, there are many examples in nature where the
gradient of a quantity has a singularity - does this count ?

Ian Taylor
http://www.iantaylor.org.uk/

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[alfansome]

For there to be an actual physical singularity it would imply infinite
density and temperature. This makes it unlikely that there are real
physical singularities. They a mathematical consequence of theory not a
real world construct.

Al.

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[the softrat]

On Thu, 15 Sep 2005 05:39:54 +0000 (UTC), "Ian Taylor"
<robert.ian.taylor@gmail.com> wrote:

>analysis problem. The "pressure spike" has also been measured
>experimentally. I have always wondered if this is a true singularity
>(in the modelled solution, not the experiment !) since when you model
>the system on a finer grid you tend to find a sharper "spike".

Sounds like what is measured, a 'sharp spike', not a true singularity.

>Quite apart from this example, which is probably completely unfamiliar
>to many on this forum, there are many examples in nature where the
>gradient of a quantity has a singularity - does this count ?
>
Nope. A 'gradient' is part of a mathematical model. What is measured
in the laboratory?

>Ian Taylor
>http://www.iantaylor.org.uk/

the softrat
Unless Barad-dur is rebuilt, twice as evil as before, Frodo has triumphed!
mailto:softrat@pobox.com
--
What if there were no hypothetical questions?

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"the softrat" wrote
> I am well aware that a number of physical models contain or predict
> singularities. My question is: Is there any experimental evidence that
> any singularity actually exists

none

> or are they all artifacts of the models?

Not artifacts, mathematical properties of a certain class of exact
solutions of the Einstein field equations.

> Lest someone jump right in with the singularity at the center of a
> black hole, let me say that, although the various solutions of
> Einstein's Equation have provided much useful guidance in
> understanding the structure of the universe, as far as I know, the
> center of a star or BH is outside of the range (or is it domain) of
> applicability of the various solutions because they presume a non-zero
> stress-energy tensor.

For the Schwarzschild and Kerr solutions the stress-energy
tensor is identical zero throughout the whole space-time.
The singularity, technically spoken, is not part of the space-time.

Of course one can ask whether a stress-energy tensor identical
to zero is physically realistic, in particular if there is Hawking
radiation, which clearly produces a non-zero energy-density
in the exterior space-time. The question of self-consistency
arises naturally in this context. The problem that the (classical)
solution we study has zero energy-density, whereas the (quantum)
physics demands non-zero energy-density, is closely related to
the highly non-trivial problem of back-reaction of Hawking
radiation.

> In point of fact, we do not know what is in
> there, we just know about the effects at and/or outside of the event
> horizon.

That is a fairly accurate description. Anything behind the
event horizon is not observable, in principle.

> It is my belief that there are no singularities in nature. I am
> looking for evidence that I am wrong.

Evidence that you are wrong would be the direct observation
of a singularity. It is quite unlikely, that this will ever happen. If
the cosmic censorship hypothesis is correct, you will never
observe a singularity directly. In this case the observational
proof of an event horizon or a trapped surface would be
indirect evidence for a singularity. Given that there are alternative
solutions for the black hole interior, that are equal to the
classical black hole solutions in the whole exterior space-time
up to a Planck length outside of the horizon, it is quite unlikely
that we can determine the difference by measurements from the
outside. We would have to send a probe into the black hole
and the probe would have to report back its finding to the
exterior observer. However, one can show that it is practically
impossible for the probe to report back when it has reached
the position where both solutions differ. The high gravitational
redshift (z^2 = 1 + r_+/r_Pl), the ultra-relativistic inward
directed velocity of the probe (gamma^2 = 1 + r_+/r_Pl)
and the phenomena associated with these special and general
relativistic phenomena (special and general relativistic time delay,
gravitational redshift, special relativistic Doppler-shift, special
relativistic aberration, the small solid angle of the general
relativistic escape cone , etc.) make it quite clear, that the probe
would have to transmit with enourmous power into an
infinitesimal solid angle. Impossible not only practically, but
also in principle, even if one takes into account that the
mass of the probe could be converted with 100% efficiency
into an outward directed signal.


> Note that renormalization in QED 'takes care of' the singularities,

You mean the "singularities" of classical electromagnetism.
These are conceptually quite different from geometrical
singularities, where the space-time structure itself brakes
down.

> i.e. they are not really there, just in an incomplete model.

maybe the model is incomplete. Maybe the solutions we
study are not the physically realistic or relevant ones...

MP

[MP]

"Kwok Man Hui" <kmhui@math.utexas.edu> wrote
>
> On Mon, 12 Sep 2005, the softrat wrote:
>
> >
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> So far, there is no direct empirical evidence of observing blackhole
> singularity.
> However, having the mathmetical prediction of blackhole singularity might
> be able to explain some cosmological phenomenon that can't be explained by
> other models. For example, billion of light year jet beam coming out of
> some discs in space.

Jets are phenomena that are related to accretion processes
onto a rotating "black hole". As such, all the processes that
power the jets have their origin in the *exterior* space-time.

Thus jets are neither a proof for the existence of an event
horizon, nor of a singularity within the hypothesized horizon.

On the other hand, the only exact solution we have found
so far, that is capable to describe the phenomena of jets,
is the Kerr (or Kerr-Newman) solution.

Therefore it is permissible to extend one's faith further
than the experimental evidence goes. This is a common
approach in physics. If a certain solution or model has
been successfully tested in some domain of interest, we
gain faith that it will remain a successful model in other
domains, which are not (yet) accessible.

> >
> I remember vaguely one of the founders of Yang-Mills gauge field theory
> said it would be Nature's mistake if it does not take such a beautiful
> theory seriously before any experimental confirmation of
> electroweak theory.

In retrospect such a statement sound very wise. Given that such
statements abound in the literature for theories or models that
have been not been successful, one should be careful to
attribute too much meaning to such statements. In the long
run it is not "beauty" but experiments that decide a contro-
versial issue.

> Be open minded.
> History has told us numerous times that it would be a mistake if some
> beautiful mathematical theories cannot be linked to some physical
> concepts.

This is the hymn that string theorists have sung, before they
adopted the anthropic principle, because the astronomers told
them that Lambda > 0. I liked the tune of string theory much
better in its original form and I think it is a pity, that string
theorists have largely abandoned their own predictions.

Maybe some day they will come to realize, what a grand
mistake this has been.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[MP]

"Igor Khavkine" wrote:
> In general, a singularity (which is not spurious, and is in principle
> measurable) indicates a failure of the theory in a given context.

or a failure of the particular solution...

unless one can prove that singularities are generic in the physical
sector of the theory.

The singularity theorems are thought to be such a proof.

However, it is mandatory to re-evaluate the assumptions on
which they are based. In the most general case (for "not overly
symmetric space-times) the assumptions are:

i) no closed time-like curves
ii) strong energy condition
iii) a trapped surface exists at some time somewhere
iv) space-time is not overly symmetric

These assumptions were thought to be reasonable at the
time the singularity theorems were discovered, except for iii)
[see e.g. MTW, Weinberg, Wald who make it quite clear that
they find the status of this assumption not as well established
as the status of the other three]

What is the status now?

i) is reasonable (causality principle)
ii) is violated by
- a cosmological constant,
- by dark energy with P < -rho/3,
- by inflation
[but is still considered a reasonable
assumption by many, who knows why]
iii) I have never found any argument that
makes it plausable that a trapped surface
must be regarded as physically reasonable
[but I would be glad to hear, if any of
you has heard of such an argument]
iv) this is quite obvious: The world is not
a sphere

> The trouble is that we have some theories that predict singularities

singularities are only predicted as generic features of the
Einstein field equations if one assumes that trapped surfaces are
physically reasonable and as long as the strong energy-condition
holds *throughout the whole space-time*. Therefore the prediction
is based on *assumptions*, one very likely violated in the past
(inflation) as well as today (accelerating universe), the other at
least doubtable from a physical perspective.

MP

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan

[kurtan]

"MP" <pet.antispam@onlinehome.de> wrote in message
news:432b2484$0$5320$9b622d9e@news.freenet.de...
> "the softrat" wrote
> > I am well aware that a number of physical models contain or predict
> > singularities. My question is: Is there any experimental evidence that
> > any singularity actually exists
>
> none
>
> > or are they all artifacts of the models?
>
> Not artifacts, mathematical properties of a certain class of exact
> solutions of the Einstein field equations.
>
> > Lest someone jump right in with the singularity at the center of a
> > black hole, let me say that, although the various solutions of
> > Einstein's Equation have provided much useful guidance in
> > understanding the structure of the universe, as far as I know, the
> > center of a star or BH is outside of the range (or is it domain) of
> > applicability of the various solutions because they presume a non-zero
> > stress-energy tensor.
>
> For the Schwarzschild and Kerr solutions the stress-energy
> tensor is identical zero throughout the whole space-time.
> The singularity, technically spoken, is not part of the space-time.
>
> Of course one can ask whether a stress-energy tensor identical
> to zero is physically realistic, in particular if there is Hawking
> radiation, which clearly produces a non-zero energy-density
> in the exterior space-time. The question of self-consistency
> arises naturally in this context. The problem that the (classical)
> solution we study has zero energy-density, whereas the (quantum)
> physics demands non-zero energy-density, is closely related to
> the highly non-trivial problem of back-reaction of Hawking
> radiation.
>
Yes, and some theorists has adressed this issue. Johan Masreliez
does it by i.a.keeping Too + T11 + T22 + T33 =0, leaving the
event horizon as sole singularity.

>
> > It is my belief that there are no singularities in nature. I am
> > looking for evidence that I am wrong.
>
> Evidence that you are wrong would be the direct observation
> of a singularity. It is quite unlikely, that this will ever happen. If
> the cosmic censorship hypothesis is correct, you will never
> observe a singularity directly. In this case the observational
> proof of an event horizon or a trapped surface would be
> indirect evidence for a singularity.
>
-------------snip
>
> maybe the model is incomplete. Maybe the solutions we
> study are not the physically realistic or relevant ones...
>
Johan Masreliez´ approach to non identically zero stress-energy
tensors and the other implications from his scale expanding FRW
model for what is generally attributed to "black holes" is treated
in his Gravitation article for the October 2004 issue of Apeiron:
http://redshift.vif.com/journal_archives.htm

If he is right we should rather be observing bubbles than BHs.

/Kurtan