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Does Hawking deserve a Nobel prize for his singularity theorem?

by petergreat
Tags: black hole, hawking, nobel, singularity
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Frame Dragger
#37
Jan24-10, 05:38 PM
P: 1,540
Quote Quote by Phrak View Post
How long does it take for a black hole to form? How long does it take for its mass to increase? What is the age of the universe? What is the theoretical justification for claiming accreation disks, jets, and other evidence of black holes are not also evidence of pre-collapsed dense masses?
A googleplex, a snifter of brandy, 42, Chocolate covered raisins, airplane's have them, Shchwarzschild metric, Kerr metric and billions of solar masses in a tiny tiny area. Wait... did I get serious at the end there? I meant... pudding.
JesseM
#38
Jan24-10, 06:27 PM
Sci Advisor
P: 8,470
Quote Quote by Phrak View Post
How long does it take for a black hole to form? How long does it take for its mass to increase? What is the age of the universe? What is the theoretical justification for claiming accreation disks, jets, and other evidence of black holes are not also evidence of pre-collapsed dense masses?
Could you answer my question about whether you are willing to accept the likelihood that GR (plus quantum field theory on curved spacetime, perhaps) is correct when dealing with energy densities far below the Planck scale? In the context of GR your questions about black holes should all have well-defined answers, but perhaps you are questioning the validity of GR itself? Or maybe you accept GR, but wish to use a coordinate system (like Schwarzschild coordinates) where it takes an infinite coordinate time for a collapsing star to actually reach the Schwarzschild limit? (if the latter, note that all coordinate systems are equally valid in GR and there are plenty of coordinate systems where you can cross the event horizon in finite time, and any particle in the star will cross the horizon in finite proper time regardless of what coordinate system you choose)
Phrak
#39
Jan24-10, 09:09 PM
P: 4,512
Quote Quote by JesseM View Post
Could you answer my question about whether you are willing to accept the likelihood that GR (plus quantum field theory on curved spacetime, perhaps) is correct when dealing with energy densities far below the Planck scale? In the context of GR your questions about black holes should all have well-defined answers, but perhaps you are questioning the validity of GR itself?
No, I am not questioning general relativity. I'm mystified as to why you are asking the set of questions you are, but in any case...

Or maybe you accept GR, but wish to use a coordinate system (like Schwarzschild coordinates) where it takes an infinite coordinate time for a collapsing star to actually reach the Schwarzschild limit? (if the latter, note that all coordinate systems are equally valid in GR and there are plenty of coordinate systems where you can cross the event horizon in finite time, and any particle in the star will cross the horizon in finite proper time regardless of what coordinate system you choose)
But not all coordinate systems are applicable. Schwarzchild coordinates are applicable to good approximation. Our clocks and telescopes are attached to the Earth or Sun system. Populate the universe with clocks and dense objects. Not one clock will record formation of an event horizon.

..in GR and there are plenty of coordinate systems where you can cross the event horizon in finite time..
Yes...relative to another coordinate system containing the the coordinate singularity--assuming we have a blackhole to start with. But this is putting the horse before the cart. The infalling clock has no event horizon to cross.

Let's assume one of your infalling coordinate systems and that the Earth is falling into a massive object. The massive object will not form an event horizon. Where are the applicable coordinate systems where we can say "lookie here. This is a picture of an accreation disk of a black hole."


I believe I've answered your questions. Will you answer mine?
JesseM
#40
Jan24-10, 10:28 PM
Sci Advisor
P: 8,470
Quote Quote by Phrak View Post
But not all coordinate systems are applicable. Schwarzchild coordinates are applicable to good approximation.
"Applicable" to what?
Quote Quote by Phrak
Our clocks and telescopes are attached to the Earth or Sun system. Populate the universe with clocks and dense objects. Not one clock will record formation of an event horizon.
What do you mean by "record formation"? Receiving light from an event on the horizon? In this case, the only clocks that will do so will be ones that cross the horizon themselves, but I don't see the problem with that.
Quote Quote by Phrak
Yes...relative to another coordinate system containing the the coordinate singularity--assuming we have a blackhole to start with. But this is putting the horse before the cart. The infalling clock has no event horizon to cross.
Do you argue that because outside observers never see infalling clocks reach some finite proper time T, that implies an observer traveling with the clock would never see it reach T or beyond?

If so, someone could make the same sort of argument about the Rindler horizon, since after all, an accelerating observer who remains outside the horizon (like one of the ones at fixed coordinate position in Rindler coordinates) will never see anything cross it, the only way to see light from an event on the Rindler horizon is to cross the horizon yourself (which should not be too surprising, since from the perspective of an inertial frame the 'Rindler horizon' is just one edge of a future light cone). Note that the relationship between Rindler coordinates (where the Rindler horizon is at fixed coordinate position and it takes an infinite coordinate time to reach it) and inertial coordinates (where the horizon is moving outward at the speed of light and can be crossed in finite time) is very closely analogous to the relationship between Schwarzschild coordinates and Kruskal-Szekeres coordinates (where the event horizon expands outward at the speed of light). So if some accelerating observer who remained forever outside the Rindler horizon seriously argued that worldlines simply "end" before reaching the proper time T where they are supposed to cross it, what would your response be? I don't see how your position is any less implausible.
Quote Quote by Phrak
Let's assume one of your infalling coordinate systems and that the Earth is falling into a massive object. The massive object will not form an event horizon.
Why do you say that? It would certainly form an event horizon in finite time in Kruskal-Szekeres coordinates, to name one. On the right side of this diagram from the Gravitation textbook by Misner/Thorne/Wheeler, you can see a collapsing star in KS coordinates, the gray area representing the interior and the black curve representing the surface, with the event horizon as the line at a 45 degree angle labeled r=2M, t=infinity (the label referring to Schwarzschild coordinates):


Quote Quote by Phrak
Where are the applicable coordinate systems where we can say "lookie here. This is a picture of an accreation disk of a black hole."
What would a coordinate system have to do with a picture? A photo isn't "native" to any particular coordinate system.
Quote Quote by Phrak
I believe I've answered your questions. Will you answer mine?
Q: How long does it take for a black hole to form?
A: Too vague. Depends if you are talking about coordinate time in some system, or proper time of some clock...and of course it also depends on physical specifics like the mass of the black hole, the point of the collapse you want to start counting down from, etc.

Q: How long does it take for its mass to increase?
A: You mean, when a new object falls in? I don't think there's any well-defined way to measure the "mass" of an extended object in a coordinate-independent way, so this would presumably depend on your choice of coordinate system too, and how you define "mass" (see this page on the difficulty in defining 'energy' in GR in a non-local sense, since mass and energy are equivalent the problems should be the same)

Q: What is the age of the universe?
A: Again depends on what coordinate system/clock you use, but the most common definition uses a coordinate system whose definition of simultaneity is such that the universe's density is about the same everywhere at a give coordinate time (the average rest frame of the cosmic microwave background radiation), and whose time coordinate matches up with the proper time of a clock that remains at rest in this system. In this case the universe's age since the Big Bang is estimated at 13.7 billion years.

Q: What is the theoretical justification for claiming accreation disks, jets, and other evidence of black holes are not also evidence of pre-collapsed dense masses?
A: Because as long as you accept GR, and you accept the principle of "geodesic completeness" which says geodesics shouldn't just "stop" at some finite proper time when it's possible to extend the spacetime manifold in a way that allows them to continue and which respects the Einstein Field Equations everywhere, then for a sufficiently massive object collapsed below a certain radius, it can be proved that an event horizon must form and that whatever's inside cannot be a stable dense mass but will collapse into a singularity (that's what the singularity theorems mentioned at the start of the thread are all about).
atyy
#41
Jan24-10, 11:17 PM
Sci Advisor
P: 8,656
Quote Quote by Phrak View Post
Where are the applicable coordinate systems where we can say "lookie here. This is a picture of an accreation disk of a black hole."

Without jumping through the horizon, the closest I've seen is to try to verify that the metric is the Kerr metric close to the event horizon "Gravitational waves would probe nonlinear gravity and could reveal small corrections, such as extra long-range fields that arise in unified theories, deviations of the metric around massive black holes from the Kerr solution ..." http://arxiv.org/abs/0903.0100
Altabeh
#42
Jan25-10, 04:56 AM
P: 665
Quote Quote by Frame Dragger View Post
If a BH loses mass through periods of NOT accreting, and emitting HR, to the point of eventual destruction (whatever form that takes) I fail to see how they can be perpetual motion machines, even in theory. They require angular momentum from their original collapsing body, or from infalling matter to rotate, and without infalling matter they slowly shrink and "get hotter". Seems like a strange thermodynamic process (or analogue thereof), but it seems limited.
It is limited and Kerr BHs can't get so much faster in their rotation than a limit of 1/72 of their total angular momentum. Don't ask how I got this limit (it is going to be explained in my PHD thesis.). So I'd guess the PMM stuff is way beyond being even wrong to believe in it!

AB
Frame Dragger
#43
Jan25-10, 05:02 AM
P: 1,540
Quote Quote by Altabeh View Post
It is limited and Kerr BHs can't get so much faster in their rotation than a limit of 1/72 of their total angular momentum. Don't ask how I got this limit (it is going to be explained in my PHD thesis.). So I'd guess the PMM stuff is way beyond being even wrong to believe in it!

AB
Well, if a Kerr BH did rotate faster, it wouldn't have an EH anymore... or am I thinking of another solutioon. Anyway, thanks very much, I never really considered before this thread that a BHH in any way could be a PMM. I look forward to your thesis btw; good luck and soon(realtively speaking of course)-to-be congratulations.
Altabeh
#44
Jan25-10, 05:30 AM
P: 665
Quote Quote by Frame Dragger View Post
Well, if a Kerr BH did rotate faster, it wouldn't have an EH anymore... or am I thinking of another solutioon. Anyway, thanks very much, I never really considered before this thread that a BHH in any way could be a PMM. I look forward to your thesis btw; good luck and soon(realtively speaking of course)-to-be congratulations.
Thank you so much. Actually my work itself makes use of Bondi mass as an infalling matter, so the BH would lose mass and therefore it would get smaller in its size but not motionless at all, but the Penrose process on the other hand gets involved to not let this happen because according to Penrose, in any case except BHs with accretion disks, the angular momentum of infalling particles decreases the total angular momentum of BH which itself is limited by the fact(?) that HR carries away angular momentum by the emission of rotating particles so it's going to make BH stop rotating. Here to have a PMM we need to know Penrose process is less happening than mine in a Kerr BH without an accretion disk. But the important thing is that in case of accretion disks, both make a BH rotate perpetually which only is possible if HR does not exist or it occurs so much slower than PP or my own process!

AB
Frame Dragger
#45
Jan25-10, 05:31 AM
P: 1,540
Quote Quote by Altabeh View Post
Thank you so much. Actually my work itself makes use of Bondi mass as an infalling matter, so the BH would lose mass and therefore it would get smaller in its size but not motionless at all, but the Penrose process on the other hand gets involved to not let this happen because according to Penrose, in any case except BHs with accretion disks, the angular momentum of infalling particles decreases the total angular momentum of BH which itself is limited by the fact(?) that HR carries away angular momentum by the emission of rotating particles so it's going to make BH stop rotating. Here to have a PMM we need to know Penrose process is less happening than mine in a Kerr BH without an accretion disk. But the important thing is that in case of accretion disks, both make a BH rotate perpetually which only is possible if HR does not exist or it occurs so much slower than PP or my own process!

AB
Elegant, I love it. Makes perfect sense too, and next to rotational frame dragging, the Penrose process is my personal favourite!
Phrak
#46
Jan25-10, 10:34 PM
P: 4,512
Quote Quote by JesseM View Post
"Applicable" to what?

What do you mean by "record formation"? Receiving light from an event on the horizon? In this case, the only clocks that will do so will be ones that cross the horizon themselves, but I don't see the problem with that.

Do you argue that because outside observers never see infalling clocks reach some finite proper time T, that implies an observer traveling with the clock would never see it reach T or beyond?

If so, someone could make the same sort of argument about the Rindler horizon, since after all, an accelerating observer who remains outside the horizon (like one of the ones at fixed coordinate position in Rindler coordinates) will never see anything cross it, the only way to see light from an event on the Rindler horizon is to cross the horizon yourself (which should not be too surprising, since from the perspective of an inertial frame the 'Rindler horizon' is just one edge of a future light cone). Note that the relationship between Rindler coordinates (where the Rindler horizon is at fixed coordinate position and it takes an infinite coordinate time to reach it) and inertial coordinates (where the horizon is moving outward at the speed of light and can be crossed in finite time) is very closely analogous to the relationship between Schwarzschild coordinates and Kruskal-Szekeres coordinates (where the event horizon expands outward at the speed of light). So if some accelerating observer who remained forever outside the Rindler horizon seriously argued that worldlines simply "end" before reaching the proper time T where they are supposed to cross it, what would your response be? I don't see how your position is any less implausible.

Why do you say that? It would certainly form an event horizon in finite time in Kruskal-Szekeres coordinates, to name one. On the right side of this diagram from the Gravitation textbook by Misner/Thorne/Wheeler, you can see a collapsing star in KS coordinates, the gray area representing the interior and the black curve representing the surface, with the event horizon as the line at a 45 degree angle labeled r=2M, t=infinity (the label referring to Schwarzschild coordinates):



What would a coordinate system have to do with a picture? A photo isn't "native" to any particular coordinate system.

Q: How long does it take for a black hole to form?
A: Too vague. Depends if you are talking about coordinate time in some system, or proper time of some clock...and of course it also depends on physical specifics like the mass of the black hole, the point of the collapse you want to start counting down from, etc.

Q: How long does it take for its mass to increase?
A: You mean, when a new object falls in? I don't think there's any well-defined way to measure the "mass" of an extended object in a coordinate-independent way, so this would presumably depend on your choice of coordinate system too, and how you define "mass" (see this page on the difficulty in defining 'energy' in GR in a non-local sense, since mass and energy are equivalent the problems should be the same)

Q: What is the age of the universe?
A: Again depends on what coordinate system/clock you use, but the most common definition uses a coordinate system whose definition of simultaneity is such that the universe's density is about the same everywhere at a give coordinate time (the average rest frame of the cosmic microwave background radiation), and whose time coordinate matches up with the proper time of a clock that remains at rest in this system. In this case the universe's age since the Big Bang is estimated at 13.7 billion years.

Q: What is the theoretical justification for claiming accreation disks, jets, and other evidence of black holes are not also evidence of pre-collapsed dense masses?
A: Because as long as you accept GR, and you accept the principle of "geodesic completeness" which says geodesics shouldn't just "stop" at some finite proper time when it's possible to extend the spacetime manifold in a way that allows them to continue and which respects the Einstein Field Equations everywhere, then for a sufficiently massive object collapsed below a certain radius, it can be proved that an event horizon must form and that whatever's inside cannot be a stable dense mass but will collapse into a singularity (that's what the singularity theorems mentioned at the start of the thread are all about).
This is going nowhere but devolving into debate. My fault of course. I did kick it off accusations of delusional beliefs. I do appreciate the response very much however, as I haven't gotten any action on this forum, on this matter without kicking the sacred cow. When I get over a full schedule of real work, moonlighting, and all-important down time, I want to post some assertions in the venue of objective science that I hope you can tear into with equal objectivity.
JesseM
#47
Jan25-10, 11:18 PM
Sci Advisor
P: 8,470
Quote Quote by Phrak View Post
This is going nowhere but devolving into debate. My fault of course. I did kick it off accusations of delusional beliefs. I do appreciate the response very much however, as I haven't gotten any action on this forum, on this matter without kicking the sacred cow. When I get over a full schedule of real work, moonlighting, and all-important down time, I want to post some assertions in the venue of objective science that I hope you can tear into with equal objectivity.
No problem, if you want to start the discussion again later when you have more time, send me a message to let me know (I haven't been hanging out on this forum as much lately so I miss a lot of threads).


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