Oppenheimer-Snyder model of star collapse

Actually, since the O-S dust has zero pressure, it can't be static.

I suspect that what O-S had in mind was something like a static star with positive pressure, in equilibrium, in which the pressure suddenly declines to zero (or at least to some negligible value compared to its previous one) over a very short time (due to, say, the stoppage of nuclear reactions in its core and a consequent sharp decline in temperature).

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.

Well, it's not for me to defend singularities' plausibility

Certainly but I was referring precisely to the static star you depict below in my answer to DS.

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?

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.

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 Lifshitz) 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 Lifshitz 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).

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.

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.

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.

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.

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.

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.

I realise that the end result BH would be spherical

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.

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

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.