[SOLVED] Is there a true singularity in nature?

"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

 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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
 "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