Oppenheimer-Snyder model of star collapse

[Mike Holland]

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

 

[PAllen]

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.

These issues are why Penrose does not consider these solutions a violation of cosmic censorship - unless someone finds a loophole that allows them to form from acceptable initial conditions.

 

[PAllen]

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

If there is any rotation at all, it is not covered by O-S (for that matter, if there is any pressure it is not governed by O-S). Even vaguely realistic collapse is only described via numeric approximations (which have become very robust and accurate in the last 10 years or so). O-S is an idealized model in the same way as SC geometry, except that it doesn't require 'eternal BH'. Instead, it provides an origin for a perfect spherically symmetric BH; as a consequence, the WH is removed, as is the wormhole to another universe.

 

[harrylin]

[..]
BTW here's the citation history of the OS paper, curious to say the least. It was ignored until 1964, but it wasn't really until the last 5 years that it took off.
http://libra.msra.cn/Publication/19921235/on-continued-gravitational-contraction

That's amazing, yes in fact it started to get more attention since 20 years ago, but even more since 6 years ago.

I had not heard of it before as I saw it cited in a recent paper as I mentioned last month*; and that paper cited it because it agrees in essence with recently expressed opinions and computer simulations.

Thanks for the graph!

*https://www.physicsforums.com/showthread.php?p=4134963&highlight=Oppenheimer#post4134963

 

[PAllen]

That's amazing, yes in fact it started to get more attention since 20 years ago, but even more since 6 years ago.

I had not heard of it before as I saw it cited in a recent paper as I mentioned last month*; and that paper cited it because it agrees in essence with recently expressed opinions and computer simulations.

Thanks for the graph!

*https://www.physicsforums.com/showthread.php?p=4134963&highlight=Oppenheimer#post4134963

If you mean Yi, his position is a crank position, not shared by any serious scholar of GR (coordinate quantities are physical; Einstein would vomit); if you mean Krauss, you misinterpret his paper seriously (applying quantum conclusions to the classical case).

[Edit: Note, you have been called out by several people here on citing only half of the O-S abstract. On the Krauss et. al. paper note the following:

"However, we find
that Schwarzschild coordinates are sufficient to answer
the very specific set of questions we ask from the asymptotic
observer’s viewpoint. Namely, does the asymptotic
observer see objects disappear into a black hole in the
time that he sees the collapsing body evaporate? And, is
the spectrum of the radiation received ever truly thermal
(even in the semiclassical approximation)?
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, we
address the problem of quantum collapse using a minisuperspace
version of the functional Schrodinger equation
[2] in Sec. IV."

All of the revisions to the classical GR results, as explained by many here, are qualified (in Krauss et.al.) by quantum corrections, and also qualified by 'see'. In this sense, this paper is scholarly, unlike the Yi paper which is crank.]

 

[harrylin]

[..] 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.

Can you put that in other words? I don't understand the "even if not" ...

 

[TrickyDicky]

Can you put that in other words? I don't understand the "even if not" ...

I was just highlighting the difference between the collapse OS model, and the Schwarzschild spacetime.

 

[harrylin]

I was just highlighting the difference between the collapse OS model, and the Schwarzschild spacetime.

Yes. And I like to know what you tried to say, as I cannot parse your sentence.

 

[TrickyDicky]

That if one imagines the future of the OS collapsing star the logic of causality, and the condition of being a solution of the EFE leads naturally to the Sch. black hole.

 

[harrylin]

That if one imagines the future of the OS collapsing star the logic of causality, and the condition of being a solution of the EFE leads naturally to the Sch. black hole.

Thus you meant: even in the OS model the logical causal future of the collapsing model is a Schwartzschild black hole with a singularity. Yes?

I think that that is wrong, or at least in contradiction with Oppenheimer-Snyder; I will check it later!

Also:

If you mean [..] crank position [..] Einstein would vomit[..]

while wrong in every aspect that post is unworthy of this forum, so I won't feed it. Insofar as it is relevant for this thread, misconceptions will become clearer in the discussion.

 

[PeterDonis]

I think that that is wrong, or at least in contradiction with Oppenheimer-Snyder; I will check it later!

My understanding is the same as TrickyDicky's: the spacetime of the O-S model contains an event horizon, black hole interior region, and future singularity. Certainly that's the way MTW describes the model; see the sections I've already referenced.

 

[TrickyDicky]

Thus you meant: even in the OS model the logical causal future of the collapsing model is a Schwartzschild black hole with a singularity. Yes?

No, the logical causal future realization is not in the OS model, but in the Sch. BH model, thus my "even if not...".

 

[PeterDonis]

No, the logical causal future realization is not in the OS model

Maybe I spoke too soon when I said our understanding was the same. If by "logical causal future realization" you mean something like you were saying before, where we somehow have to substitute the full maximally extended Schwarzschild spacetime for the O-S collapsing spacetime, that is *not* correct. I thought you just meant that the O-S model's spacetime contains a future horizon, a BH interior vacuum region, and a future singularity, in addition to the region occupied by the collapsing matter. And I should add that my understanding is that those regions I just listed are the *entire* spacetime; there is nothing else, so there is no past horizon and no white hole region. The maximally extended Schwarzschild spacetime contains a past horizon and white hole, but the O-S spacetime does *not*.

 

[PeterDonis]

The maximally extended Schwarzschild spacetime contains a past horizon and white hole, but the O-S spacetime does *not*.

I can't remember if this particular page on Hamilton's site has been linked to in this thread, but it shows a Penrose diagram of the O-S model:

http://casa.colorado.edu/~ajsh/collapse.html#penrose

Compare with the Penrose diagram of the maximally extended Schwarzschild geometry here:

http://online.kitp.ucsb.edu/online/colloq/hamilton1/oh/penrose_Schwpar.html

 

[harrylin]

Thus you meant: even in the OS model the logical causal future of the collapsing model is a Schwartzschild black hole with a singularity. Yes?

I think that that is wrong, or at least in contradiction with Oppenheimer-Snyder; I will check it later! [..]

My understanding is the same as TrickyDicky's: the spacetime of the O-S model contains an event horizon, black hole interior region, and future singularity. Certainly that's the way MTW describes the model; see the sections I've already referenced.

I don't have MTW but I do have O-S, which is what matters; see next.

No, the logical causal future realization is not in the OS model, but in the Sch. BH model, thus my "even if not...".

OK. I now checked it more carefully, and I maintain the paper essentially agrees with Einstein's paper of that same year; however I had not noticed that it is in fact a bit inconsistent. Still, the paper denies for forming black holes the future realisation of a singularity; thus "collapse" in the summary apparently refers to the shrinking to its gravitational radius. Here are the IMHO pertinent passages (I hope that I cite little enough not to infringe copyright):

Near the surface of the star,
where the pressure must in any case be low, we
should expect to have a local observer see matter
falling inward with a velocity very close to that
of light; to a distant observer this motion will be
slowed up by a factor (1-r_o/r_b). All energy
emitted outward from the surface of the star
will be reduced very much in escaping, by the
Doppler effect from the receding source, by the
large gravitational red-shift, (1-r_o/r_b)^½, and by
the gravitational deflection of light which will
prevent the escape of radiation except through a
cone about the outward normal of progressively
shrinking aperture as the star contracts. The star
thus tends to close itself off from any communi-
cation with a distant observer; only its gravi-
tational field persists.
[..]
Further, a star
in its early stage of development would not
possess a singular density or pressure; it is
impossible for a singularity to develop in a finite
time.
[..]
we see that for a fixed
value of R as t tends toward infinity, τ tends to a
finite limit, which increases with R. After this
time τ_o an observer comoving with the matter
would not be able to send a light signal from the
star; the cone within which a signal can escape
has closed entirely.

 

[PeterDonis]

I don't have MTW but I do have O-S, which is what matters

It does if we are trying to establish what O-S said in their original paper, yes. But there is also a separate question, which is, what is the best currently accepted "O-S" model, i.e., the best currently accepted spacetime that models the collapse of a massive object like a star? We may be talking past each other if you are trying to answer the first question while I am trying to answer the second, and the answers are different (see below).

OK. I now checked it more carefully, and I maintain the paper essentially agrees with Einstein's paper of that same year; however I had not noticed that it is in fact a bit inconsistent. Still, the paper denies for forming black holes the future realisation of a singularity; thus "collapse" in the summary apparently refers to the shrinking to its gravitational radius.

Hm, yes, I see what you mean; they don't seem fully consistent in what they say, and this language doesn't seem fully consistent with the abstract. So it may indeed be that the answers to the two questions above are different. I can't say for sure without seeing the whole paper. If the answers are different, then we have indeed been talking past each other, since I have been talking about question #2, the best current model, in the belief that (as presented in MTW) that was also the model O-S had derived. For example, the Penrose diagram I posted a link to in my last post was for the best current model.

(I hope that I cite little enough not to infringe copyright)

A side note, off-topic but this is a pet peeve of mine: the fact that you even have to worry about this is outrageous. If only they had had arxiv.org in 1939...

 

[PAllen]

I don't have MTW but I do have O-S, which is what matters; see next.

Unfortunately, it remains a bit difficult to interpret these snippets without the fuller context, which you obviously can't provide (and which most of us here cannot access). However, it seems quite possible to interpret these snippets as given in a way perfectly consistent with the modern understanding of O-S collapse:

OK. I now checked it more carefully, and I maintain the paper essentially agrees with Einstein's paper of that same year; however I had not noticed that it is in fact a bit inconsistent. Still, the paper denies for forming black holes the future realisation of a singularity; thus "collapse" in the summary apparently refers to the shrinking to its gravitational radius. Here are the IMHO pertinent passages (I hope that I cite little enough not to infringe copyright):

Near the surface of the star,
where the pressure must in any case be low, we
should expect to have a local observer see matter
falling inward with a velocity very close to that
of light; to a distant observer this motion will be
slowed up by a factor (1-r_o/r_b). All energy
emitted outward from the surface of the star
will be reduced very much in escaping, by the
Doppler effect from the receding source, by the
large gravitational red-shift, (1-r_o/r_b)^½, and by
the gravitational deflection of light which will
prevent the escape of radiation except through a
cone about the outward normal of progressively
shrinking aperture as the star contracts. The star
thus tends to close itself off from any communi-
cation with a distant observer; only its gravi-
tational field persists.

I don't see anything wrong with this description. I see it as not even addressing the question of what happens to the infalling matter. It simply says, whatever happens is unable to causally influence (in any way) a distant observer. This is indisputable.

[..]
Further, a star
in its early stage of development would not
possess a singular density or pressure; it is
impossible for a singularity to develop in a finite
time.

There are two parts to this. Early : no singularity; obvious, no dispute.
For the second part, the issue is 'whose time, defined or measured how'. Much more context would be needed to resolve this.

[..]
we see that for a fixed
value of R as t tends toward infinity, τ tends to a
finite limit, which increases with R. After this
time τ_o an observer comoving with the matter
would not be able to send a light signal from the
star; the cone within which a signal can escape
has closed entirely.

The last is perfectly consistent with my understanding.

The upshot is these quotes leave me convinced that were I to read the paper, I would find it mostly agreeing with modern understanding.

As for modern understanding, since MTW is not accessible on line, with some effort, I found the following, which gives a really good introduction to dust collapse:http://www.aei.mpg.de/~rezzolla/lnotes/mondragone/collapse.pdf

Chapters 3 and 4 give a good treatment, with both illustrations and explanations that can be somewhat separated from the math, if that is too much for the reader (though the level is easier than MTW, at least in this section). See, especially, the illustration at the top of p. 31.

[Edit: Final note: Even if we could all access the O-S paper, and concluded some statements disagreed with later understandings, this would be purely of historic interest. There are not multiple versions of GR equations; nor multiple definitions of physical observables (right from 1915, Einstein defined these invariant quantities computed from covariant objects). On the other hand, mathematical technique and results are cumulative. It is not shocking to say an early practitioner was mistaken about some consequence of the theory. Einstein, for example, flip flopped 3 times on whether gravitational waves were a real prediction of his theory - ending with the view that they definitely were.]

 

[PeterDonis]

I don't see anything wrong with this description. I see it as not even addressing the question of what happens to the infalling matter. It simply says, whatever happens is unable to causally influence (in any way) a distant observer. This is indisputable.

I agree. I didn't mean to imply that I thought what harrylin quoted was inconsistent with modern understanding; what he quoted clearly states that the proper time experienced by an infalling observer riding on the surface of the collapsing star, from a finite radius R down to the horizon, is finite. That's the modern understanding. I was only saying that I had thought the O-S paper itself addressed what happens *after* the infalling matter reaches the horizon; but it appears it may not.

[Edit: Final note: Even if we could all access the O-S paper, and concluded some statements disagreed with later understandings, this would be purely of historic interest.

I agree; that's why I made a point of drawing a distinction between my question #1--what is the model presented in the original O-S paper?--and question #2--what is the best current model? Everything I have said in this thread is really directed at #2, not #1.

 

[Mike Holland]

http://www.aei.mpg.de/~rezzolla/lnotes/mondragone/collapse.pdf

Thanks for that reference, PAllen. It answers my queries about rapidly rotating disc-like collapsing stars.
I shall continue lurking around your discussion.
Mike

 

[harrylin]

[..] the proper time experienced by an infalling observer riding on the surface of the collapsing star, from a finite radius R down to the horizon, is finite. That's the modern understanding. [..]

I'm surprised to hear that there ever was a different understanding about the proper time of the infalling observer; I did not find any disagreement on that point in the literature. Do you have a reference to such a paper?

 

[PAllen]

I'm surprised to hear that there ever was a different understanding about the proper time of the infalling observer; I did not find any disagreement on that point in the literature. Do you have a reference to such a paper?

I wouldn't say there was ever a disagreement, but the fact wasn't known (as far as I know) before the O-S paper, and not well known for 20 years later. Note, what Peter is referring to is an observer following a collapsing surface - not the test trajectory for an SC geometry. Collapse was not understood to any degree before the O-S paper. Even the behavior of test trajectories to or through an SC geometry EH wasn't at all well known until the late 1930s.

Also, note that Einstein's paper of the same year as O-S argued that no real collapse could ever happen as envisaged in the O-S paper. Modern understanding is that Einstein's argument was simply wrong; while the O-S paper is viewed as the simplest case that has the general characteristics of realistic collapse analyzed by numerical GR (and is also consistent with the singularity theorems).

 

[harrylin]

I wouldn't say there was ever a disagreement, but the fact wasn't known (as far as I know) before the O-S paper [..]

OK

Also, note that Einstein's paper of the same year as O-S argued that no real collapse could ever happen as invisaged in the O-S paper. Modern understanding is that Einstein's argument was simply wrong; while the O-S paper is viewed as the simplest case that has the general characteristics of realistic collapse analyzed by numerical GR (and is also consistent with the singularity theorems).

Contrary to you, I noted no essential difference between those two papers; the O-S paper doesn't describe what you would call a "real collapse". Further, I can see no way to counter the arguments in those papers; and I have seen no counter argument in any peer reviewed paper or in the recent discussions here, nor in the discussion about the more recent understanding on the other forum to which I gave the link.

 

[PAllen]

OK

Contrary to you, I noted no essential difference between those two papers; the O-S paper doesn't describe what you would call a "real collapse". Further, I can see no way to counter the arguments in those papers; and I have seen no counter argument in any peer reviewed paper or in the recent discussions here, nor in the discussion about the more recent understanding on the other forum to which I gave the link.

That's because many here interpret those papers differently from you. I see the O-S paper (from its abstract) arguing for a real collapse that is not seen by an outside observer. Consensus source available on line discussing this exact same mathematics agree with this. Einstein argued, on the contrary, that this solution could not be realized in the real world - it was not a matter of how to interpret a solution but an argument that the O-S solution (without being mentioned by name) would not actually occur from a reasonable starting point. Einstein's argument in this particular paper is generally recognized as wrong.

As for the Krauss paper, I have read it twice; I and others here disagree with your interpretation. To me it says:

- Authors review aspects of the classical collapse. Wording is very careful to convey (to me) that nothing new or different from consensus is claimed here. Certain aspects are emphasized. It is emphasized that, by pure choice (not physical significance - classically) they are using SC t=constant slices; these are qualified in the intro section to be just a choice useful to the paper's overall purpose:

- Quantum mechanical arguments are presented to show that the EH never actually forms when quantum phenomena are considered; specifically evaporation rates.

I also disagree with your view of the status of this paper. It has the status of an interesting contribution, not a consensus, even for the quantum features. There are literally hundreds of papers in the last 5 years offering many different takes on how QM modifies the classical GR collapse process. This paper is just one respectable contribution to that.

 

[George Jones]

OK. I now checked it more carefully, and I maintain the paper essentially agrees with Einstein's paper of that same year;

See below.

however I had not noticed that it is in fact a bit inconsistent. Still, the paper denies for forming black holes the future realisation of a singularity;

As others have noted, this is just plain wrong.

Also, note that Einstein's paper of the same year as O-S argued that no real collapse could ever happen as envisaged in the O-S paper. Modern understanding is that Einstein's argument was simply wrong; while the O-S paper is viewed as the simplest case that has the general characteristics of realistic collapse analyzed by numerical GR (and is also consistent with the singularity theorems).

In his 1939 paper, Einstein drew the wrong conclusion from his calculations. What he actually showed (or came close to showing) was that, below the event horizon, Schwarzschild spacetime is not stationary.

 

[harrylin]

[..]
As others have noted, this is just plain wrong.

Hi George, please elaborate: 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". 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.

In his 1939 paper, Einstein drew the wrong conclusion from his calculations. What he actually showed (or came close to showing) was that, below the event horizon, Schwarzschild spacetime is not stationary.

That paper is a bit off topic so I won't elaborate on that. Just one question, in view of your claim: do you (or anyone else) know a paper that proves that he drew the wrong conclusion?
Thanks in advance!

 

[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.