Oppenheimer-Snyder model of star collapse


by TrickyDicky
Tags: collapse, model, oppenheimersnyder, star
PAllen
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Nov18-12, 01:08 PM
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Quote Quote by harrylin View Post
I don't know what you mean with "region in the spacetime"; that seems to be a technical term. But that doesn't matter, as you can decide for yourself:

As already mentioned in the latest thread, section III of http://arxiv.org/abs/gr-qc/0609024
Section three of that paper contains nothing new, and its authors don't claim anything new in this section (they footnote these results to an ancient paper by Townsend). They use this formalism to then establish new results using quantum methods.
PAllen
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Nov18-12, 01:16 PM
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Quote Quote by harrylin View Post
Apart of an untreatable mutual misunderstanding, we absolutely agree on this. Distant clock time is only physical reality in the sense that a distant clock must indicate a time, which in principle allows for verification of predictions.
There is in principle nothing that prevents us from putting clocks in orbit around a black hole, approximately tuned to the ECI coordinate system.
Of course we can put clocks all over in different states of motion, and modify their 'natural readings' as desired. However (and maybe you don't disagree) it remains purely a matter of convention or definition which reading on one clock is considered 'the same time' as which reading on another clock.

Note, we can readily do this between an infalling clock and a distant clock such that 3 pm on both clocks corresponds to the infalling clock a microsecond before hitting the singularity. Each clock would read its own proper time, and the relation between their world lines would be based on GP time coordinate instead of SC time coordinate (the time coordinate just being used to establish simultaneity relations).
harrylin
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Quote Quote by PAllen View Post
Section three of that paper contains nothing new, and its authors don't claim anything new in this section (they footnote these results to an ancient paper by Townsend). [..]
Indeed, as we already discussed in this thread, their opinion, already from their "classical" analysis, that "the horizon does not form in a finite time" is nothing new; and as I already mentioned in the new thread, Kraus pretends that it is "controversial" - which is obviously true, as can be seen by the reactions to their publication by some on this forum. I will not elaborate on it in this thread, as that would distract from the O-S model.
PAllen
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Nov18-12, 01:31 PM
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Quote Quote by harrylin View Post
Indeed, as we already discussed in this thread, their opinion, already from their "classical" analysis, that "the horizon does not form in a finite time" is nothing new; and as I already mentioned in the new thread, Kraus pretends that it is "controversial" - which is obviously true, as can be seen by the reactions to their publication by some on this forum. I will not elaborate on it in this thread, as that would distract from the O-S model.
If you look carefully, the word 'controversial' in that part of the quote is the journalist's word not Kraus's word. The part actually quoted to Kraus is non-controversial. Again, nothing said in the paper or any of the commentary you link to is inconsistent with:

- starting from established classical results, wondering if one way causality and behavior of SC coordinate time may provide a hint at quantum treatment,

- we then treat the the collapse quantum mechanically (using SC coordinates) and find that evaporation beats collapse. Therefore the information paradox never arises. And backfitting this result, we may choose to ignore anything classical GR says about the horizon and interior.

And counter arguing papers are all on the second bullet above: you don't escape the information paradox that easily. Evaporation does not beat collapse. A deeper solution to the information paradox is needed.
PeterDonis
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Nov18-12, 03:18 PM
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Quote Quote by harrylin View Post
I'm not sure what you mean with "is there a black hole region in the spacetime"; that seems to be a technical term.
I suppose it could be called technical, but it's not very technical. Look at the diagram that DrGreg posted of a spherically symmetric gravitational collapse. The blue region in that diagram is the "black hole region", and it is part of the spacetime because it appears on the diagram. That's all "there is a black hole region in the spacetime" means.

But since the blue region is above the horizon line (the 45 degree line going up and to the right), light signals from the black hole region can never get out to the gray region, which is the region covered by the distant observer's time coordinate. That's why the black hole region is not "visible" to the distant observer; he can never see light signals from it. But the region is there.

Quote Quote by harrylin View Post
Probably you will conclude that in their model there isn't one, if you use the same definitions as them in their press statement.

As already mentioned in the latest thread, section III of http://arxiv.org/abs/gr-qc/0609024
This section does give a "classical model", but in that model, there *is* an event horizon and a black hole region; it's just not visible to the asymptotic observer (because no light signals from the EH or the BH region can get back out to the asymptotic observer). In other words, it's qualitatively the same as what I have been calling the best current classical GR model of gravitational collapse. If you drew a spacetime diagram of it in the appropriate coordinates, it would look similar to DrGreg's diagram, including the blue region.
PeterDonis
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Quote Quote by harrylin View Post
There is in principle nothing that prevents us from putting clocks in orbit around a black hole, approximately tuned to the ECI coordinate system.
But you won't be able to extend the ECI coordinates inside the horizon; they will become singular at the horizon just like standard Schwarzschild coordinates do. So ECI coordinates won't cover the black hole region.
PAllen
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Nov18-12, 08:21 PM
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Quote Quote by harrylin View Post
Indeed, as we already discussed in this thread, their opinion, already from their "classical" analysis, that "the horizon does not form in a finite time" is nothing new; and as I already mentioned in the new thread, Kraus pretends that it is "controversial" - which is obviously true, as can be seen by the reactions to their publication by some on this forum. I will not elaborate on it in this thread, as that would distract from the O-S model.
Forget journalism and press releases (though it is clear to me you misinterpret the press release). Here is the brief description of the results of section III by the author's intended for a scientific audience:

"In Sec. III we verify the standard result that the formation
of an event horizon takes an infinite (Schwarzschild)
time if we consider classical collapse. This is not
surprising and is often viewed as a limitation of the
Schwarzschild coordinate system. To see if this result
changes when quantum effects are taken into account.."

Let me emphasize:

- verify standard results

- infinite Schwarzschild time

No where are they claiming a new classical result; no where do they dispute (nor mention) the classical result that the in other coordinates the EH happens in finite coordinate time, and that the dust cloud crosses the EH in finite time for a clock following just above its surface. These are not concerns of the paper. The paper is clearly concerned with quantum corrections, wherein (if they are right) these other features go away. They believe in coordinate invariance, so the implication is that if quantum analysis says the collapsed object evaporates before the EH is formed in SC coordinates, then this means, in any coordinates, and for any observer, there is no EH at all. This is the new and fairly radical claim - all based on quantum corrections. If piece of matter transforms to radiation before a horizon is formed in coordinate system, the fact must be true in all. This is the controversial aspect of their work.

[Edit: in reference to Dr. Greg's beautiful illustration in #64, the key point of the Krauss,et.al. paper is to argue that [due to quantum behavior - evaporation], the grey line curves up asymptotically to the top 45 degree line of the pink region, never entering the blue region. This means the blue region is not part of the solution at all. This is all coordinate independent geometry. The claim is not about interpreting something like classical O-S spacetime; it is that, when quantum effects are considered, classical O-S spacetime does not occur. What does occur looks very much like it, for a distant observer, for a very long time, but eventually, it can be distinguished - via the radiation - that the actual spacetime was never similar to an O-S spacetime, in that the blue region never existed - at all, for any observer.

If we translate the Krauss et. all. proposal to the experience of an observer on the collapsing shell, we get, instead of:

- reaching a horizon, then a singularity, in finite clock time (for that observer)

we get:

- being converted to not quite thermal radiation, in finite clock time, without ever reaching the critical radius.

If their result holds, and also applies to dust ball collapse, as they hope it does, then an interior observer of such a collapse would experience:

- in finite time, evaporating to non quite thermal radiation before reaching a minimum radius.
]
PeterDonis
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Nov18-12, 09:36 PM
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Quote Quote by PAllen View Post
in reference to Dr. Greg's beautiful illustration in #64, the key point of the Krauss,et.al. paper is to argue that [due to quantum behavior - evaporation], the grey line curves up asymptotically to the top 45 degree line of the pink region, never entering the blue region. This means the blue region is not part of the solution at all.
PAllen, great summary. The only point I would add is that, in reference to DrGreg's diagram, it's not enough for just the grey line to curve up and to the right as you describe; the entire interior of the collapsing matter has to do so. DrGreg did not show that region in his diagram; the grey line is just the outer surface of the collapsing matter.

As I read it, the model in the Krauss paper is somewhat different from the "O-S" model (by which I mean the modern version, not necessarily the version in the O-S paper). The Krauss paper models a collapsing "domain wall", which means a very thin spherical shell of stress-energy. In this model, the grey line in DrGreg's diagram *would* indeed be the entire "collapsing matter", since that matter is supposed to be very thin. Obviously this is much less realistic, physically, than the collapse of spherically symmetric dust as in the standard O-S type model (which itself is highly idealized, of course, with zero pressure and perfect spherical symmetry). They appear to be willing to make the educated guess that the qualitative conclusions from their model would still hold in a more realistic model; but they don't actually show that.

However, that leaves a very big open question in my mind: what is *inside* the domain wall? The classical GR conclusion would be that it is a flat Minkowski spacetime region, which would shrink as the domain wall collapses. However, I don't see such a region included in the Krauss paper's model at all. I haven't read any of the papers making counter-arguments, so I don't know if this issue has been raised.

Just off the top of my head, including the flat region interior to the domain wall, if the conclusion of Krauss et al. is true that quantum effects stop the collapse by converting the domain wall's stress-energy into outgoing radiation before it forms a horizon, would change the whole spacetime diagram; it would no longer look like DrGreg's. (Actually, if Krauss et al. are correct and a horizon doesn't form when quantum effects are included, that would change the diagram in any case; the 45 degree line up and to the right is the horizon, and if there is no horizon that changes the whole causal structure.) This is probably getting pretty far off topic for this thread, though.
PAllen
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Nov18-12, 09:58 PM
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Quote Quote by PeterDonis View Post
Just off the top of my head, including the flat region interior to the domain wall, if the conclusion of Krauss et al. is true that quantum effects stop the collapse by converting the domain wall's stress-energy into outgoing radiation before it forms a horizon, would change the whole spacetime diagram; it would no longer look like DrGreg's. (Actually, if Krauss et al. are correct and a horizon doesn't form when quantum effects are included, that would change the diagram in any case; the 45 degree line up and to the right is the horizon, and if there is no horizon that changes the whole causal structure.) This is probably getting pretty far off topic for this thread, though.
The main refutation seems to be the long Padnanabhan paper I linked. I have only skimmed it and much of it is too far beyond my expertise to read. However, they do raise, as one of several errors, that, if Krauss et.al. are right about the evaporation process, then they are wrong about using exterior SC geometry, even if spherical symmetry is assumed (due to the radiation).

Without radiation, and without a horizon, you could still the geometry as a large part of Dr. Greg's pink region. The grey line would bend up below the 'horizon that isn't there'. Anything outside (left of) the grey line would not be SC geometry, and we could cover it with a different chart. However, the remaining pink part could still represent the exact SC geometry outside the non-collapsing shell.
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Nov18-12, 10:49 PM
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Quote Quote by PAllen View Post
The main refutation seems to be the long Padnanabhan paper I linked. I have only skimmed it and much of it is too far beyond my expertise to read. However, they do raise, as one of several errors, that, if Krauss et.al. are right about the evaporation process, then they are wrong about using exterior SC geometry, even if spherical symmetry is assumed (due to the radiation).
Ok, that means I didn't guess too badly.

Quote Quote by PAllen View Post
Without radiation, and without a horizon,
Does this make sense? Isn't the Krauss argument that the horizon doesn't form because the stress-energy in the collapsing domain wall gets converted into radiation? If there is no radiation, what stops the horizon from forming?

Quote Quote by PAllen View Post
The grey line would bend up below the 'horizon that isn't there'. Anything outside (left of) the grey line would not be SC geometry, and we could cover it with a different chart. However, the remaining pink part could still represent the exact SC geometry outside the non-collapsing shell.
I see the general point, but I'm not sure about it, because the "shape" of the pink region depends on their being a horizon; if the upward 45 degree line isn't there, because the horizon isn't there, there is no reason for the grey line to "bend up below the horizon that isn't there". There is no singularity "above" the horizon line if quantum effects mean the horizon doesn't form, so with no horizon timelike lines could extend "upwards" indefinitely and still be able to send light signals to infinity.
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Quote Quote by PeterDonis View Post
Does this make sense? Isn't the Krauss argument that the horizon doesn't form because the stress-energy in the collapsing domain wall gets converted into radiation? If there is no radiation, what stops the horizon from forming?
mass of shell too small
Quote Quote by PeterDonis View Post
I see the general point, but I'm not sure about it, because the "shape" of the pink region depends on their being a horizon; if the upward 45 degree line isn't there, because the horizon isn't there, there is no reason for the grey line to "bend up below the horizon that isn't there". There is no singularity "above" the horizon line if quantum effects mean the horizon doesn't form, so with no horizon timelike lines could extend "upwards" indefinitely and still be able to send light signals to infinity.
I have SC geometry for r > r0 for some r0 > SC radius (where Birkhoff applies). Within this region I use SC coordinates. Now, I apply the transform to Kruskal for this region of spacetime. I get section of Dr. Greg's pink region to the right of the r0 curve.
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Quote Quote by PAllen View Post
mass of shell too small
But the shell is collapsing; if radiation doesn't continually carry away its mass, eventually it will collapse far enough to form a horizon. If there's no radiation, there's no method of carrying away any of its mass, so it will *have* to eventually form a horizon, regardless of how small its mass is; that's the point of the classical analysis in section III of the paper.

Quote Quote by PAllen View Post
I have SC geometry for r > r0 for some r0 > SC radius (where Birkhoff applies). Within this region I use SC coordinates. Now, I apply the transform to Kruskal for this region of spacetime. I get section of Dr. Greg's pink region to the right of the r0 curve.
Yes, I understand that; I'm just trying to understand what the rest of the spacetime would look like (the part occupied by the non-collapsing wall and the interior Minkowski region) in these coordinates. Probably I need to first think about a simpler case, a static spherically symmetric star surrounded by vacuum, and how that would look when transformed to Kruskal-like coordinates.
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Quote Quote by PeterDonis View Post
But the shell is collapsing; if radiation doesn't continually carry away its mass, eventually it will collapse far enough to form a horizon. If there's no radiation, there's no method of carrying away any of its mass, so it will *have* to eventually form a horizon, regardless of how small its mass is; that's the point of the classical analysis in section III of the paper.
I haven't looked at whether they exclude pressure from the Lagrangian. However, for any realistic equation of state for matter, there is a shell mass below which collapse will simply stop at some point. Dr. Greg referred to this possibility. It is also discussed at some length in the Padmanabhan paper, where they show some claims of the Krauss et.al. paper lead to rather silly conclusions for this case.
Quote Quote by PeterDonis View Post

Yes, I understand that; I'm just trying to understand what the rest of the spacetime would look like (the part occupied by the non-collapsing wall and the interior Minkowski region) in these coordinates. Probably I need to first think about a simpler case, a static spherically symmetric star surrounded by vacuum, and how that would look when transformed to Kruskal-like coordinates.
I was positing a simpler way of handling it. Use the section of Kruskal I described for a vacuum. Use a completely different chart for the non-vacuum. For the non-vacuum, you must satisfy junction conditions. However, Birkhoff allows you to ignore that for the vacuum part.
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Quote Quote by PAllen View Post
I haven't looked at whether they exclude pressure from the Lagrangian. However, for any realistic equation of state for matter, there is a shell mass below which collapse will simply stop at some point. Dr. Greg referred to this possibility. It is also discussed at some length in the Padmanabhan paper, where they show some claims of the Krauss et.al. paper lead to rather silly conclusions for this case.
Hm, yes, I wasn't considering pressure. I'll have to look at the paper again to see exactly how they model the domain wall; I had thought it was simply a shell of dust, but I may be wrong.

Quote Quote by PAllen View Post
I was positing a simpler way of handling it. Use the section of Kruskal I described for a vacuum. Use a completely different chart for the non-vacuum.
There's nothing requiring the use of a specific chart, true. The standard Kruskal chart only works for vacuum regions anyway. But in order to show the causal structure of the spacetime, I would want to find a chart for the non-vacuum region that still shows radial null curves as 45 degree lines; I don't know if such a chart has ever been used. [Edit: Actually a Penrose chart does this, and those do exist for FRW spacetimes, so one can certainly draw one for the standard O-S type model where an FRW interior is matched to a Schwarzschild exterior; I've seen that done. I haven't seen one for a "domain wall" type of model.]
harrylin
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Nov19-12, 10:59 AM
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Quote Quote by PAllen View Post
[..] you don't escape the information paradox that easily. Evaporation does not beat collapse. A deeper solution to the information paradox is needed.
I had not seen this. Contrary to you, I can find no paradox at all, except with your interpretation.
But probably we will discuss that in your new thread, http://www.physicsforums.com/showthread.php?t=652839
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Quote Quote by harrylin View Post
I had not seen this. Contrary to you, I can find no paradox at all, except with your interpretation.
But probably we will discuss that in your new thread, http://www.physicsforums.com/showthread.php?t=652839
The 'information paradox' is a general concern of quantum mechanics + gravity. It is universally accepted that there must be some solution (well, except for Penrose, who believes information is truly lost in a BH, and QM must be superseded). A great many possible solutions have been proposed. As I read the Krauss et.al. paper and other paper citing it, it is proposal in this general field: the information paradox is resolved because it never occurs, because the collapsed object evaporates before EH is formed. Most other solutions involve quantizing the EH (and interior) in some way, with various models of how the information paradox gets solved in the particular model.

But again, as seem so common, I am not sure I understand what your are getting at. Probability of this seems 99% bidirectional between us.
harrylin
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Nov21-12, 07:09 AM
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Quote Quote by PAllen View Post
[..] But again, as seem so common, I am not sure I understand what your are getting at. Probability of this seems 99% bidirectional between us.
Yes, that is too often a problem. But not this time: I made sure to not clarify it here, because I want to discuss it there - and knowing you, if I clarify it here then you will start to discuss it here.
harrylin
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Nov23-12, 03:09 AM
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Quote Quote by harrylin View Post
[..] probably we will discuss that in your new thread, http://www.physicsforums.com/showthread.php?t=652839
The discussion there was for me very surprising. The discussion quickly zoomed in on O-S model predictions - and that brings me back to this thread:
Quote Quote by harrylin View Post
they consider Schwarzschild coordinate time to be far away clock time - which is approximately the time on our clocks. And that time is according to GR valid for making physical predictions, just as they did and I cited.
Quote Quote by PeterDonis View Post
[SC coordinate map] is valid for making physical predictions about the region of spacetime in which that time coordinate is finite. It is *not* valid for making physical predictions about any other region of spacetime.
Quote Quote by PeterDonis View Post
The only sense in which the maps "disagree about events" is that one map (SC coordinates) can't assign coordinates to some events (those on or inside the horizon), while another map (e.g., Painleve coordinates) can.
Quote Quote by PAllen View Post
Actually they don't disagree about events. With one convention, assign remote times ranging to infinity for all the events I will ever see. I still compute that physical law says there are other events I will never actually see.
Quote Quote by PeterDonis View Post
Time codes emitted from Earth are received by Voyager just fine at τ=42, and indeed all the way up to τ=48.
Inspired by that last comment, I will here expand on that simple example.

Voyager 35 is sent to a newly discovered black hole only about 20 light years away and which for simplicity we assume to be eternal static, and in rest wrt the solar system. The Voyager is indestructible and always in operation.

A time code is emitted from Earth that can be received by Voyager. Voyager emits its proper time code s1 that is sent back to Earth together with the then received time stamp t1 from Earth (we'll ignore the technical difficulties).

An observer on Earth with the name Kraus calculates the expected (s1,t1) signal from Voyager as function of expected UTC, for the approximation or assumption that the black hole is completely formed. He stresses that he could choose other coordinates, but that the "SC" of Oppenheimer-Snyder-1939 are fine and valid for making predictions about what can be observed on Earth, making small corrections for Earth's gravitational field and orbit. He finds something like the following (I pull this out of my hat, just for the gist of it):

UTC , (s1 , t1)
--------------
100 , 40.3, 200
1E3 , 41.2, 1.5E3
1E4 , 41.5, 1E5
1E5 , 41.7, 1E7
1E6 , 41.9, 1E10
1E100 42.0, 1E1000

My question: Please give an illustration of time codes t1 from Earth that reach Voyager at τ=43, as it has gone through the horizon.


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