Oppenheimer-Snyder model of star collapse

[PeterDonis]

according to O-S, and consistent with their preceding discussion, for a star that does not yet "possess a singular density or pressure" "it is impossible for a singularity to develop in a finite time".

In this paragraph of the paper, O-S are using "time" to mean what we now call "Schwarzschild coordinate time". Slightly later they call it "clock time at r = infinity", and they also use the coordinate t to refer to it. The precise way to express what they are saying here, in modern language, is that the density and pressure of the collapsing star can never become singular in the region of spacetime where Schwarzschild coordinate time is finite (and timelike--even more precisely, we would say "exterior Schwarzschild coordinate time" to make it clear that we are talking about the region outside the horizon, and outside the collapsing matter as long as it is above the horizon).

But you say that it is "plain wrong" to think that this means that the future realisation of a singularity does not happen for forming black holes. Surely infinite time doesn't happen, so I don't follow your thinking.

The correct way to say "infinite time doesn't happen" is "Schwarzschild coordinate time never becomes infinite anywhere along the worldline of the distant observer". That is *not* the same as saying "the region of spacetime in which the worldline of the distant observer lies, and in which Schwarzschild coordinate time is finite, is the entire spacetime". The latter statement is false. The "future realization of a singularity" happens in a different region of spacetime, one which the coordinate chart in which Schwarzschild coordinate time (strictly speaking, *exterior* Schwarzschild coordinate time) is finite does not cover.

 

[harrylin]

In this paragraph of the paper, O-S are using "time" to mean what we now call "Schwarzschild coordinate time". Slightly later they call it "clock time at r = infinity", and they also use the coordinate t to refer to it. The precise way to express what they are saying here, in modern language, is that the density and pressure of the collapsing star can never become singular in the region of spacetime where Schwarzschild coordinate time is finite (and timelike--even more precisely, we would say "exterior Schwarzschild coordinate time" to make it clear that we are talking about the region outside the horizon, and outside the collapsing matter as long as it is above the horizon).

Yes, 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. I understand the language of O-S better than your "modern language". As far as I understand your "modern" paraphrase of what they wrote, it agrees with mine; you just put it in "modern" wrapping. But if not, please correct my paraphrase in standard English.

The correct way to say "infinite time doesn't happen" is "Schwarzschild coordinate time never becomes infinite anywhere along the worldline of the distant observer".

Why would you think that "infinite time doesn't happen" could be incorrect? It simply means that no clock (at least, no clock that is tuned in accordance with theory) will ever indicate ∞.

That is *not* the same as saying "the region of spacetime in which the worldline of the distant observer lies, and in which Schwarzschild coordinate time is finite, is the entire spacetime". The latter statement is false. [..]

Obviously.

The "future realization of a singularity" happens in a different region of spacetime, one which the coordinate chart in which Schwarzschild coordinate time (strictly speaking, *exterior* Schwarzschild coordinate time) is finite does not cover.

In my language your claim is incompatible with the claim of O-S; apparently we don't speak the same language. So be it. I hope to have clarified that Trickydicky's "logical causal future realization" is according to O-S "impossible to develop in a finite time" - with which of course not the proper clock time of an infalling observer is meant, but approximately our clock time.

 

[PAllen]

Yes, 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. I understand the language of O-S better than your "modern language". As far as I understand your "modern" paraphrase of what they wrote, it agrees with mine; you just put it in "modern" wrapping. But if not, please correct my paraphrase in standard English.

Why would you think that "infinite time doesn't happen" could be incorrect? It simply means that no clock (at least, no clock that is tuned in accordance with theory) will ever indicate ∞.

Obviously.

In my language your claim is incompatible with the claim of O-S; apparently we don't speak the same language. So be it. I hope to have clarified that Trickydicky's "logical causal future realization" is according to O-S "impossible to develop in a finite time" - with which of course not the proper clock time of an infalling observer is meant, but approximately our clock time.

A key problem is your insistence that only one type of clock matters, as opposed examining the universe using all clocks. A clock just outside the dust ball, free falling with it, encounters the singularity if finite time. There is no justification for subtracting this clock from reality.

Another key problem is considering any coordinate time physical. All coordinate times can be used to make physical predictions, but no coordinate time, by itself, constitutes a physical prediction or observable quantity - especially even Minkowski coordinate time for inertial observers in SR. The predictions are what is measured by various observers.

The type of one-way causal relations between distant, static, observers and free fall observers is a common characteristic of pseudo-riemannian metrics, and can occur purely in SR, as has been explained a zillion times. The relations between a distant clock and free fall clock in SC geometry has virtually identical features as the relation between a uniformly accelerating observer and an inertial observer in SR, with the distant observer playing the role of the uniformly accelerating observer.

[Edit: Let me try to clarify further between a coordinate statement (of no physical significance whatsoever) versus a statement about observables.

1) Coordinate statement: For distant observer's time, an event horizon never forms. Why is this not a physical statement? Both SR and GR completely reject the concept of global time as a physical concept. Global time is construct of convention or convenience, in all cases. This misleading statement has buried within it a concept there is physical meaning to distant simultaneity : which events in universe correspond to which times on a distant clock. As I have explained numerous times, there are perfectly plausible alternative (to SC coordinate time based simultaneity) simultaneity conventions which relate events inside the horizon to events on distant clocks.

2) Indisputable physical statements: No physical process at or inside the horizon can causally influence a distant observer, even if that distant observer's world line is continued to infinite proper time (while remaining 'distant'). Conversely, distant observers can causally influence infallers up to the moment of their reaching the singularity. In a Kerr black hole (assuming its exact interior actually existed in our universe - it is definitely a predicted possibility of GR), where there are stable interior orbits, an external observer can send messages to such an interior orbiting observer forever; they just can't get a reply.

The difference between (1) and (2) may be subtle, but it is crucial. Note that, as required diffeomorphism invariance, Kruskal coordinates predict (2) just as much as SC coordinates. Further, a simultaneity surface relating interior and exterior event can be defined in SC coordinates; you just need to use limiting processes at the horizon due to the coordinate singularity there.

]

 

[DrGreg]

I haven't read the O-S paper and am not prepared to spend $25 to do so, but it seems to me most of the discussion in this thread isn't about the fine details of O-S collapse, but about more fundamental issues.

If we assume we have a non-rotating uncharged spherically symmetric distribution of matter surrounded by vacuum, then Birkhoff's Theorem tells us that the Schwarzschild solution must apply throughout the vacuum region, which means the vacuum region must look something like this:

The pink grid shows the exterior Schwarzschild coordinates. The blue grid shows the interior Schwarzschild coordinates (that is, inside the event horizon, but still outside the collapsing matter). The purple dotted line is the event horizon. The thick blue line is the singularity. All of these have been plotted accurately using MATLAB and are mandated by Birkhoff's theorem, regardless of the details of the collapse.

The grey line from the bottom to the left is the border of the vacuum region, i.e. the outermost layer of the collapsing matter. It is not possible to continue the diagram to the left of this line because Schwarzschild coordinates do not apply there. I have only sketched an approximate location for this line. The precise shape of this line will depend on the details of the collapse. The O-S model and other models would produce different shapes for the grey curve. But the pink and blue grid to the right of the line is the same for all models that are compatible with my initial assumptions.

If the collapse were resisted by sufficient pressure to prevent the event horizon forming, the grey curve would remain entirely within the pink region and would curve towards the top right of diagram. Otherwise, the curve must enter the blue region and eventually hit the darker blue singularity.

I have drawn this as a Kruskal–Szekeres diagram. There is an invisible, uniformly square, horizontal and vertical grid of Kruskal–Szekeres coordinates not shown. The advantage of a Kruskal–Szekeres diagram is that it shares many features with a Minkowski diagram in flat spacetime: timelike directions are within 45° of vertical, spacelike directions are within 45° of horizontal, and light travels at exactly 45°. The difference is scale. Minkowski maps have a uniform scale: the ratio of 1 cm vertically on the map to 1 second in the Universe is constant, and the ratio of 1 cm horizontally on the map to 1 light-second in the Universe is constant. On a Kruskal–Szekeres map, the map scale is variable (although at every event, the horizontal and vertical scales are the same as each other).

The pink curves are the worldlines of observers hovering at a constant distance from the centre of the collapsing matter, and the radial pink lines are lines of simultaneity for such observers as determined by the convention of Schwarzschild coordinates. For these observers, none of the events in the blue region occur "simultaneously" with an event on the observer's worldline, so you could say the event "never occurs" (within finite time) relative to that observer. But that is just an artefact of the coordinate system chosen. It's unreasonable to say those events "don't exist".

 

[PeterDonis]

Yes, 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.

It's 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.

Why would you think that "infinite time doesn't happen" could be incorrect? It simply means that no clock (at least, no clock that is tuned in accordance with theory) will ever indicate ∞.

Yes, no actual clock will ever give an infinite reading. But that does not mean that any clock which gives a finite reading has to be confined to the region of spacetime where the Schwarzschild time coordinate is finite. Clocks don't read coordinate time, they read proper time along their worldlines. Only clocks "at infinity" actually read that time coordinate, because only for clocks "at infinity" is Schwarzschild coordinate time equal to proper time along their worldlines.

In my language your claim is incompatible with the claim of O-S; apparently we don't speak the same language. So be it. I hope to have clarified that Trickydicky's "logical causal future realization" is according to O-S "impossible to develop in a finite time" - with which of course not the proper clock time of an infalling observer is meant, but approximately our clock time.

I'm confused. Are we talking about physics or terminology? I don't care what terminology you use; I'm just trying to figure out whether we disagree about the physics or not.

When O-S (and you) use the words "impossible to develop in a finite time", that can have two meanings:

#1: It doesn't happen anywhere in the region of spacetime covered by the Schwarzschild exterior time coordinate, but it does happen in some *other* region of spacetime.

#2: It doesn't happen *anywhere* in the spacetime, period.

If all you mean is #1, then we agree on the physics; we just disagree on the terminology we're using to describe it. If you mean #2, we disagree on the physics.

It's possible that O-S themselves did not take a position in their paper on this question; in other words, it's possible that all O-S meant by "impossible to happen in a finite time" was this:

#0: It doesn't happen anywhere in the region of spacetime covered by the Schwarzschild exterior time coordinate; we take no position on whether it happens in some other region of spacetime, because our model only covers the region covered by finite values of Schwarzschild coordinate time, and we haven't studied the question of whether or not the spacetime contains other regions besides that one.

But even if it was the case that O-S meant #1, I don't care; I have already said I agree with PAllen that that's a question about history, not physics. Our best current model of gravitational collapse says #1 is true and #2 is false; that's what I mean by "the physics".

 

[harrylin]

A key problem is your insistence that only one type of clock matters, as opposed examining the universe using all clocks.[..]

As I clarified earlier, not at all; you continue to misrepresent what I say. Instead I stressed that in GR all reference systems are valid for the predictions of physics. However, it suddenly becomes really interesting:

Let me try to clarify further between a coordinate statement (of no physical significance whatsoever) versus a statement about observables.

1) Coordinate statement: For distant observer's time, an event horizon never forms. Why is this not a physical statement? Both SR and GR completely reject the concept of global time as a physical concept. Global time is construct of convention or convenience, in all cases. This misleading statement has buried within it a concept there is physical meaning to distant simultaneity : which events in universe correspond to which times on a distant clock.
2) Indisputable physical statements [..]

Here we have a subtle but fundamental disagreement, even concerning SR. You pretend that global coordinate time cannot be used as a physical concept for making predictions about physical events, not even in SR. However, I know with 100% certainty that according to SR the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good (this was restricted to inertial frames). Those laws are for making predictions about observable events. And I think that the same is true according to GR, including accelerating frames. If you like, we can start that as a topic; it is too far off topic to discuss here.

 

[harrylin]

It's 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. [..]

Yes of course - that is the only thing that is needed.

Yes, no actual clock will ever give an infinite reading. But that does not mean that any clock which gives a finite reading has to be confined to the region of spacetime where the Schwarzschild time coordinate is finite. Clocks don't read coordinate time, they read proper time along their worldlines. Only clocks "at infinity" actually read that time coordinate

In fact, that is our free choice. In 1911, while developing GR, Einstein proposed that "we must use clocks of unlike constitution, for measuring time at places with differeing gravitational potential". That is in practice exactly what is done based on GR, and there is nothing in theory (both in GR and in theory) to prevent us from doing so for the whole accessible universe.

I'm confused. Are we talking about physics or terminology?

I thought that we were talking about physics; however I found myself being told that what I say is "wrong", without however identifying anything substantial apart of the fact that I do not use modern jargon.

When O-S (and you) use the words "impossible to develop in a finite time", that can have two meanings:

#1: It doesn't happen anywhere in the region of spacetime covered by the Schwarzschild exterior time coordinate, but it does happen in some *other* region of spacetime.

#2: It doesn't happen *anywhere* in the spacetime, period.

Here we discuss not our opinions but that of O-S, and about what follows from their model.
As I mentioned earlier, there appear to be some inconsistencies in formulation in their paper, which made me doubt that O-S had contemplated that question when they wrote it. For that reason I did not make a statement that goes beyond what they explained; my point was that Trickydicky made a claim about O-S that I find hard to rime with what O-S claimed themselves.

It's possible that O-S themselves did not take a position in their paper on this question; in other words, it's possible that all O-S meant by "impossible to happen in a finite time" was this:

#0: It doesn't happen anywhere in the region of spacetime covered by the Schwarzschild exterior time coordinate; we take no position on whether it happens in some other region of spacetime, because our model only covers the region covered by finite values of Schwarzschild coordinate time, and we haven't studied the question of whether or not the spacetime contains other regions besides that one.

Yes, that almost matches my opinion, except that perhaps they had not yet developed that thought - I suppose that they would have made such a statement if they had.

But even if it was the case that O-S meant #1, I don't care; I have already said I agree with PAllen that that's a question about history, not physics. Our best current model of gravitational collapse says #1 is true and #2 is false; that's what I mean by "the physics".

Concerning modern models, I have not yet been won over to consider option #1 as possibly physical; that makes option #2 more plausible for me, at least for from the outside infalling matter. And as you know that option was promoted 5 years ago by Vachaspati et al in phys. review D. However, I cannot judge the quality of their model, or how well their non-QM simulation matches the O-S model. That's just my 2cts.
Once more, the blog of their university: http://blog.case.edu/case-news/2007/06/20/blackholes

 

[PAllen]

Here we have a subtle but fundamental disagreement, even concerning SR. You pretend that global coordinate time cannot be used as a physical concept for making predictions about physical events, not even in SR. However, I know with 100% certainty that according to SR the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good (this was restricted to inertial frames). Those laws are for making predictions about observable events. And I think that the same is true according to GR, including accelerating frames. If you like, we can start that as a topic; it is too far off topic to discuss here.

Here is how subtle things are: I absolutely agree and have explicitly stated numerous times that any coordinate time is valid for making physical predictions. But since this is true for any coordinate time, to me (and, I absolutely believe, Einstein, but not necessarily Lorentz), the implications is none can be physically preferred, and none have physical meaning beyond convention (thus Einstein's careful use in e.g. his 1905 paper: we stipulate; we define; the pure conventions are separated from physical predictions).

So, to you: useful for making physical predictions = physical reality. To me, this follows only if the thing under discussion is, itself, observable. The statement 'my time at a distant place' is not a physically verifiable statement at all. The statement: if I assign time to distant events in one of many ways, I can readily compute physical predictions: this is indisputable. Since nothing more can be given verifiable meaning, I believe nothing more than this.

 

[PAllen]

And as you know that option was promoted 5 years ago by Vachaspati et al in phys. review D. However, I cannot judge the quality of their model, or how well their non-QM simulation matches the O-S model. That's just my 2cts.
Once more, the blog of their university: http://blog.case.edu/case-news/2007/06/20/blackholes

What part of this is non-quantum? As I read it, none is non quantum because it all based on radiation computed using functional schrodinger formalism. We seem to read English differently.

 

[PeterDonis]

In fact, that is our free choice. In 1911, while developing GR, Einstein proposed that "we must use clocks of unlike constitution, for measuring time at places with differeing gravitational potential". That is in practice exactly what is done based on GR, and there is nothing in theory (both in GR and in theory) to prevent us from doing so for the whole accessible universe.

Yes, it's our free choice what clocks to use and what worldlines they follow. But it is *not* our free choice, once the clocks and worldlines are given, to decide what those clocks will read. That's determined by physics. It's also not our free choice what regions of spacetime are present, and what kinds of relationships are possible between the readings on clocks following worldlines that become spatially separated; that's also determined by physics.

Concerning modern models, I have not yet been won over to consider option #1 as possibly physical; that makes option #2 more plausible for me, at least for from the outside infalling matter.

Huh? It's a simple question: is there an event horizon and black hole region anywhere in the spacetime, or not? "Modern models" give an unequivocal answer for the case of classical GR (no quantum corrections): yes. Any paper, whether it's "modern" or not, that claims otherwise is not a reputable paper (or else you're misunderstanding the paper to be talking about the classical case when it's actually talking about the quantum case--see below).

There is not an unequivocal answer when quantum corrections are included; but the O-S paper was not about the quantum case, it was about the classical case, so for this thread, I was assuming that any "modern models" we wanted to talk about would also be about the classical case, not the quantum case. If we want to talk about the quantum case we should probably start a separate thread.

And as you know that option was promoted 5 years ago by Vachaspati et al in phys. review D. However, I cannot judge the quality of their model, or how well their non-QM simulation matches the O-S model. That's just my 2cts.
Once more, the blog of their university: http://blog.case.edu/case-news/2007/06/20/blackholes

This is talking about the quantum case, not the classical case. What "non-QM simulation" are you referring to? I don't see any such thing here.

 

[harrylin]

Here is how subtle things are: I absolutely agree and have explicitly stated numerous times that any coordinate time is valid for making physical predictions. But since this is true for any coordinate time, to me (and, I absolutely believe, Einstein, but not necessarily Lorentz), the implications is none can be physically preferred, and none have physical meaning beyond convention (thus Einstein's careful use in e.g. his 1905 paper: we stipulate; we define; the pure conventions are separated from physical predictions).

So, to you: useful for making physical predictions = physical reality. To me, this follows only if the thing under discussion is, itself, observable. The statement 'my time at a distant place' is not a physically verifiable statement at all. The statement: if I assign time to distant events in one of many ways, I can readily compute physical predictions: this is indisputable. Since nothing more can be given verifiable meaning, I believe nothing more than this.

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.

 

[harrylin]

[..] Huh? It's a simple question: is there an event horizon and black hole region anywhere in the spacetime, or not? "Modern models" give an unequivocal answer for the case of classical GR (no quantum corrections): yes. Any paper, whether it's "modern" or not, that claims otherwise is not a reputable paper (or else you're misunderstanding the paper to be talking about the classical case when it's actually talking about the quantum case--see below).

I'm not sure what you mean with "is there a black hole region in the spacetime"; that seems to be a technical term. Probably you will conclude that in their model there isn't one, if you use the same definitions as them in their press statement. You can decide for yourself:

[..] What "non-QM simulation" are you referring to? I don't see any such thing here.

As already mentioned in the latest thread, section III of http://arxiv.org/abs/gr-qc/0609024

 

[PAllen]

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]

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]

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]

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]

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.

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]

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]

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]

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]

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.

 

[PeterDonis]

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.

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?

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.

 

[PAllen]

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

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.

 

[PeterDonis]

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.

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.

 

[PAllen]

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.

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.

 

[PeterDonis]

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.

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]

[..] 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, https://www.physicsforums.com/showthread.php?t=652839

 

[PAllen]

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, https://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]

[..] 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]

[..] probably we will discuss that in your new thread, https://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:

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.

[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.

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.

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.

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.