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Oppenheimer-Snyder model of star collapse

by TrickyDicky
Tags: collapse, model, oppenheimersnyder, star
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DaleSpam
#19
Nov12-12, 05:13 PM
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Quote Quote by TrickyDicky View Post
Certainly but I was referring precisely to the static star you depict below in my answer to DS.
All the OS model insists is that at some moment there is a spherical dust cloud which is momentarily at rest. There is certainly no implication in the OS model that the "static star" has been in such a state since before the big bang.

Plausibility is definitely subjective, so you can choose to disagree. However, to me it is clear that a model which begins from a momentarily stationary sphere of dust is more plausible than a model which begins from a singularity. We have direct experience with things that approximate a momentarily stationary sphere of dust, but not with singularities. So the opposite stance seems tenuous.
TrickyDicky
#20
Nov12-12, 05:40 PM
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Quote Quote by DaleSpam View Post
All the OS model insists is that at some moment there is a spherical dust cloud which is momentarily at rest. There is certainly no implication in the OS model that the "static star" has been in such a state since before the big bang.

Plausibility is definitely subjective, so you can choose to disagree. However, to me it is clear that a model which begins from a momentarily stationary sphere of dust is more plausible than a model which begins from a singularity. We have direct experience with things that approximate a momentarily stationary sphere of dust, but not with singularities. So the opposite stance seems tenuous.
Well, it's not for me to defend singularities' plausibility, or GR's for that matter, you are free to have whatever opinion, I can only refer you to the Hawking-Penrose singularity theorems.
DaleSpam
#21
Nov12-12, 07:30 PM
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Quote Quote by TrickyDicky View Post
Well, it's not for me to defend singularities' plausibility
Hmm, I thought that was exactly what you were attempting to do in your OP. Are you not claiming that Schwarzschild is more plausible than OS?
PeterDonis
#22
Nov12-12, 09:28 PM
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Quote Quote by TrickyDicky View Post
Certainly but I was referring precisely to the static star you depict below in my answer to DS.
That's fine, but AFAIK it's not part of the "O-S model" as standardly understood, which is why your use of the phrase "OS collapsing star is a static object" confused me.
TrickyDicky
#23
Nov13-12, 02:43 AM
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Quote Quote by DaleSpam View Post
Hmm, I thought that was exactly what you were attempting to do in your OP. Are you not claiming that Schwarzschild is more plausible than OS?
As I said this is a subjective issue in great part, and I have not presented in such simple terms, on the contrary, I was trying to show how the opposite claim by PeterDonis needed some qualifications to have any meaning other than the subjective preference.
One of this qualifications I tried to explain was that even if not in the OS model the logical causal future of the collapsing model is a BH with a singularity, and for the non-charged, non-rotating case the only mathematical model we have of that is an exact solution of the EFE is the extended Schwarzschild spacetime.
pervect
#24
Nov13-12, 03:09 AM
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Quote Quote by TrickyDicky View Post
One of this qualifications I tried to explain was that even if not in the OS model the logical causal future of the collapsing model is a BH with a singularity, and for the non-charged, non-rotating case the only mathematical model we have of that is an exact solution of the EFE is the extended Schwarzschild spacetime.
We also have the BKL solutions. Kip Thorne, for one, believes that they are likely to represent actual physical collapse. (This was metioned in his semi-popular book, "Black Holes & Timewarps").

http://en.wikipedia.org/w/index.php?...ldid=490892346 has a brief discussion. I'm not terribly familiar with the details of the BKL solution other than it's very chaotic, Wiki gives the references. Wiki talks about BKL in the context of the early universe, I'd assume time-reversing that gives the solution Kip Thorne is fond of.
TrickyDicky
#25
Nov13-12, 04:16 AM
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Quote Quote by pervect View Post
We also have the BKL solutions. Kip Thorne, for one, believes that they are likely to represent actual physical collapse. (This was metioned in his semi-popular book, "Black Holes & Timewarps").

http://en.wikipedia.org/w/index.php?...ldid=490892346 has a brief discussion. I'm not terribly familiar with the details of the BKL solution other than it's very chaotic, Wiki gives the references. Wiki talks about BKL in the context of the early universe, I'd assume time-reversing that gives the solution Kip Thorne is fond of.
As you mention BKL is a model of evolution of the Universe near the initial singularity, usually applied to cosmological models and time singularities rather than to the spacelike singularities of BHs.
I have not read Thorne's semipopular book, so I don't know how or in what context he applied the BKL model in the BH setting.
pervect
#26
Nov13-12, 07:03 AM
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Here's a relevant quote, from pg 473, about BKL sigularities

Recall that Oppenheimer and Snyder gave us clear and unequivocal answers to our three questions. When the black hole is created by a highly idealized, spherical, imploding star, then (1) everything that enters the hole gets swallowed by the singularity; (2) nothing travels to another universe or another part of our universe; (3) when nearing the singularity, evertthing eperiences an infinitely growing radial stretch and transverse squeeze (Fig 13.1) and thereby gets destroyed.

This answer was pedagogically useful; it helped motivate calculations that brought deeper understanding. However, the deeper understanding (due to Khalatnikov and Lifgarbagez) showed that the Oppenhimer Snyder answer is irrelveant to the real Universe in which we live, because the random defomations that occur in all real stars will completely change the holes interior. The Oppenhiemer Synyder interiior is "unstable against small pertubations".

....

Belinsky, Khalatnikov, and Lifgarbagez hae given us yet another answer to our questions, and this one, being totally stable against small pertubations, is probaby the "right" answer, the answer that applies to the real black holes that inhabit our Universe: [b]The star that form the hole and everything that falls into the hole when the hole is young get torn apart by the tidal gravity of a BKL singularity.[b]. (This is the kind of singularity that Belinksky, Khalatnikov, and Lifhitz discovered, as a solution of Einstein's equation, after Penrose convinced hem that singularites must inhabit black holes).
So there you have it. Thorne mentioned that this was his thinking ca 1993 earlier in the text, a section I dont want to take the time to quote. I don't know if he's changed his mind since then, he's indicated that he's open to changing his mind on this issue, which is worth mentioning, I think. But it's reasonably clear (to me at least) that it's wrong to say we don't have solutions other than the Oppenheimer Snyder ones.
DaleSpam
#27
Nov13-12, 07:15 AM
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Quote Quote by TrickyDicky View Post
As I said this is a subjective issue in great part, and I have not presented in such simple terms, on the contrary, I was trying to show how the opposite claim by PeterDonis needed some qualifications to have any meaning other than the subjective preference.
OK, I misunderstood. I thought you were making the claim that the S model is more plausible than the OS model.

Quote Quote by TrickyDicky View Post
One of this qualifications I tried to explain was that even if not in the OS model the logical causal future of the collapsing model is a BH with a singularity, and for the non-charged, non-rotating case the only mathematical model we have of that is an exact solution of the EFE is the extended Schwarzschild spacetime.
How does that impact the plausibility? It doesn't seem relevant to me.

IMO, physical plausibility of a model is defined by two factors: are the laws governing the evolution of the model consistent with experiment and are the boundary conditions possible. Here, the laws are the same, the EFE, so they are equally plausible wrt the first factor. Second, the OS boundary conditions are an idealized but reasonable approximation of observed situations, the S boundary conditions have never been directly observed. So OS is more plausible wrt the second factor. I simply don't see the relevance of any of the other points you have brought up. Neither the historical development of the models, nor the fact that the models are closely related, nor any other point you have mentioned seem to have any bearing on plausibility, IMO.
TrickyDicky
#28
Nov13-12, 08:18 AM
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Quote Quote by pervect View Post
Here's a relevant quote, from pg 473, about BKL sigularities



So there you have it. Thorne mentioned that this was his thinking ca 1993 earlier in the text, a section I dont want to take the time to quote. I don't know if he's changed his mind since then, he's indicated that he's open to changing his mind on this issue, which is worth mentioning, I think. But it's reasonably clear (to me at least) that it's wrong to say we don't have solutions other than the Oppenheimer Snyder ones.
I said no other solution specifically for the future of the OS model of collapsing star, BLK solution is clearly according to Thorne a more plausible alternative for the OS model itself, more stable, for the collapsing star near the singularity, but after reading some excerpts from amazon it's clear his explanation involves a big dose of speculation as Thorne himself admits, I don't know how much has survived in the last 20 years from the book publication.
PeterDonis
#29
Nov13-12, 09:23 AM
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Quote Quote by pervect View Post
But it's reasonably clear (to me at least) that it's wrong to say we don't have solutions other than the Oppenheimer Snyder ones.
Yes, you're right, I wasn't taking into account the BKL solutions in my original post in this thread.

Quote Quote by TrickyDicky View Post
BLK solution is clearly according to Thorne a more plausible alternative for the OS model itself, more stable, for the collapsing star near the singularity, but after reading some excerpts from amazon it's clear his explanation involves a big dose of speculation as Thorne himself admits, I don't know how much has survived in the last 20 years from the book publication.
There's an article on living reviews about the BKL model:

http://relativity.livingreviews.org/...ticlesu11.html

There's a lot of high-powered math here, but it at least appears to illustrate that the BKL model is still an active area of research (at least as of 2008) and is still considered valid; from section 2.9 of the article:

"We shall assume throughout our review that the BKL description is correct, based on the original convincing arguments put forward by BKL themselves"

This sentence is footnoted with a reference to BKL's original paper.
PeterDonis
#30
Nov13-12, 09:40 AM
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Quote Quote by TrickyDicky View Post
As you mention BKL is a model of evolution of the Universe near the initial singularity, usually applied to cosmological models and time singularities rather than to the spacelike singularities of BHs.
Just a quick comment: any BKL singularity is spacelike, including the initial singularity in the BKL cosmological model (as well as the final singularity in a BKL model of stellar collapse). (The initial singularity in a perfectly spherically symmetric expanding FRW model is also spacelike; I'm not aware of any cosmological model with a timelike singularity.)
Mike Holland
#31
Nov13-12, 07:39 PM
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Excuse me butting in here, but I have a big concern about the O-S calculation. You all keep agreeing that it applies to a spherical symmetric collapsing mass. But when you think about how fast a pulsar spins, in general a near-BH mass would spin very much faster, and at best we would have an oblate spheroid. In fact, what I have in mind would look something like an LP record! I realise that the end result BH would be spherical, but I don't see how it can be spherical beore reaching that stage except in very idealised theory.

If this picture is correct, then mass in the polar direction would have very little distance to fall, but there would be very little of it, while the angular momentum of the equatorial regions would delay the collapse significantly. Is this taken into account in any of the calculations that have been done?

A further note - such a flat spinning object would qualify as an axi-symmetric collapse as described by Saul Teukolsky, in which one could at some stage have a naked singularity before the Black Hole forms completely.

I would like to hear your comments.

Mike
PeterDonis
#32
Nov13-12, 10:13 PM
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Quote Quote by Mike Holland View Post
You all keep agreeing that it applies to a spherical symmetric collapsing mass.
Because that is an assumption of the O-S model.

Quote Quote by Mike Holland View Post
But when you think about how fast a pulsar spins, in general a near-BH mass would spin very much faster, and at best we would have an oblate spheroid.
If a BH is formed by a process similar to how a spinning pulsar is formed, yes, one would expect it to be spinning fast. The O-S model is not meant to apply to this case.

Quote Quote by Mike Holland View Post
I realise that the end result BH would be spherical
No, it wouldn't. A spinning BH is not spherical; it's an oblate spheroid. More precisely, its horizon is shaped like an oblate spheroid.

Quote Quote by Mike Holland View Post
If this picture is correct, then mass in the polar direction would have very little distance to fall, but there would be very little of it, while the angular momentum of the equatorial regions would delay the collapse significantly. Is this taken into account in any of the calculations that have been done?
I'm sure there are numerical models of a collapse with significant angular momentum, which is basically what you're describing. I don't think there is any analytical solution for this case. As I said above, the O-S model was not intended to apply to this case; it was a drastically idealized model that was constructed in order to be able to find an analytical solution whose qualitative properties could be investigated. It was not meant to model a "realistic" stellar collapse.

Quote Quote by Mike Holland View Post
A further note - such a flat spinning object would qualify as an axi-symmetric collapse as described by Saul Teukolsky, in which one could at some stage have a naked singularity before the Black Hole forms completely.
If there is enough angular momentum compared to the total mass, yes, I believe there could be a naked singularity. In this case, however, I don't think a BH ever forms (meaning I don't think a horizon ever forms). I believe this is the case where the angular momentum per unit mass is large enough to be what the Wikipedia page calls an "over-extreme Kerr solution":

http://en.wikipedia.org/wiki/Kerr_me...Kerr_solutions

These solutions have no horizon, just a naked singularity.
PAllen
#33
Nov13-12, 10:37 PM
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Quote Quote by Mike Holland View Post
Excuse me butting in here, but I have a big concern about the O-S calculation. You all keep agreeing that it applies to a spherical symmetric collapsing mass. But when you think about how fast a pulsar spins, in general a near-BH mass would spin very much faster, and at best we would have an oblate spheroid. In fact, what I have in mind would look something like an LP record! I realise that the end result BH would be spherical, but I don't see how it can be spherical beore reaching that stage except in very idealised theory.

If this picture is correct, then mass in the polar direction would have very little distance to fall, but there would be very little of it, while the angular momentum of the equatorial regions would delay the collapse significantly. Is this taken into account in any of the calculations that have been done?

A further note - such a flat spinning object would qualify as an axi-symmetric collapse as described by Saul Teukolsky, in which one could at some stage have a naked singularity before the Black Hole forms completely.

I would like to hear your comments.

Mike
The claim is only that it is more realistic model of BH than SC eternal WH-BH. There is no dispute that it is still extremely unrealistic for the reason you mention - no rotation. Once there is rotation, there is no spherical symmetry.

Teukolsky's model is theoretically very interesting, but also unrealistic - any deviation, however slight, from perfect axial symmetry removes the naked singularity (this is why Penrose's revised bet is still unclaimed - a naked singularity from initial conditions that are perturbatively stable). The best bet for realism are numerical simulations. Whatever the details of collapse, the final, stable form long after last matter infall, is simply the Kerr-Newman metric, at least on the outside. The inside is another matter, that has been discussed above by Pervect.

Please note: this whole line of siscussion would be distraction for this thread, which was opened specifically to discuss Oppenheimer-Snyder.
PAllen
#34
Nov13-12, 10:40 PM
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Quote Quote by PeterDonis View Post
If there is enough angular momentum compared to the total mass, yes, I believe there could be a naked singularity. In this case, however, I don't think a BH ever forms (meaning I don't think a horizon ever forms). I believe this is the case where the angular momentum per unit mass is large enough to be what the Wikipedia page calls an "over-extreme Kerr solution":

http://en.wikipedia.org/wiki/Kerr_me...Kerr_solutions

These solutions have no horizon, just a naked singularity.
I could be wrong, but I recall reading papers showing that an over-extreme Kerr-Newman cannot form. That is, it exists mathematically like a WH solution, but cannot arise from matter satisfying any of the energy conditions, no matter what initial conditions.
PeterDonis
#35
Nov13-12, 11:53 PM
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Quote Quote by PAllen View Post
I recall reading papers showing that an over-extreme Kerr-Newman cannot form.
I vaguely recall reading speculations along these lines (not actual papers). It seems reasonable to me; I also seem to remember that there is a theorem along the lines of: you can't make a Kerr BH into an over-extreme Kerr geometry by adding angular momentum to it; you always end up adding enough mass along with the angular momentum to keep the angular momentum per unit mass below the limit.
Mike Holland
#36
Nov14-12, 06:00 AM
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Quote Quote by PAllen View Post
Please note: this whole line of discussion would be distraction for this thread, which was opened specifically to discuss Oppenheimer-Snyder.
That is a joke after what happened to my "Black Holes - two points of view" thread - a long argument about Killing Vectors! I just abandoned that thread!

I thought my post was about O-S black hole formation. But anyway, thanks for your replies. I shall read up more on Kerr's ideas and their follow-ons. I am particularly interested in the effects of perturbations in the various models, and in numerical simulations of BH formation, but I don't have the maths to follow the calculations.

Mike


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