Speed of light enough to escape black holes ?

PAllen
According to me, a worldline cannot observe. Anyway, I still wonder why the emission frequency would be positive and real (from a distant perspective of course) instead of imaginary as with the approximate solution:
To me, a detector (which follows a world line) is the only thing that can observe. Coordinate labels and simultaneity are abstractions, not observables. So any detector that can observe light emitted inside the EH observes red or blueshift following normal GR rules. The general GR rule is to parallel transport the emitter 4-velociy to the receiver world line along the light path followed. Then express the transported emitter 4 velocity and local light path tangent vector in the local frame basis of the reception event, and use SR doppler formula. This formulation covers every combination of kinematic and curvature and cosmological contribution to redshift in one general method.

The concept of a gravitational redshift 'field' as in that wikipedia formula is a special case that applies only to static space time. It is doubly nonsensical to apply it across the event horizon:
1) There are no emitter and receiver possible from the inside to outside the EH. Therefore it is applied outside its domain of validity.

2) You can't even write an alternative equivalent formula for inside the horizon because the region inside the horizon is not static, so there is no such thing, even approximately, of a gravitational potential. The concept of gravitational redhsift factored out separately from general redshift as I described above is possible only for static spacetime.

One final key point: for emitter outside EH and receiver inside EH, you can compute the red/blue shift using the standard method I describe and get a perfectly normal result - because there is a light path from emitter to receiver in this case. The result cannot be summarized into a redhift as a function of position for the very reason above: the light path goes from a static region of spacetime to a non-static region.

I'm sorry if all of these realities of GR are ignored in wikipedia level treatments, but I can assure you they were well understood by 1960.
I have followed some of those threads without participating: the parts that I saw exactly avoided addressing such issues as this one. And it looks as if you formulated it better (more precisely) last time:

"They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. [..] "

If you transform that description of yours to our distant ECI frame, I suspect that you will find that to our reckoning, those signals of us will reach that person shortly before t=∞ so that "an instant before reaching the singularity" transforms to "perhaps after the end of this universe". But if that is wrong, please clarify why.
There is no such thing as a global frame in GR. There are local frames and global coordinate systems. So your statement asks for something GR states does not exist.

The best you can do in GR is define a family non-intersecting spacelike 3-surfaces of simultaneity that you parametrize with a timelike parameter. SC coordinates do this in a way that covers only the exterior region of a BH. Lemaitre and Kruskal coordinates do this in a way that covers the whole spacetime. Each provides a specific (and different) answer to what events inside the horizon are simultaneous with a given event outside.

Each of these coordinate systems (Lemaitre and Kruskal) provide a finite well defined answer to 'when', for an outside observer, a signal reaches a given inside detector.

Short answer: your question reflects fundamental misunderstanding of GR; corrected in the only way I know, your conclusion is wrong.
That may be well the case. I think that there will be even much less misunderstanding if you or someone else would be so kind to express those events in "earth coordinates", which would clarify if in theory this topic relates to something that can ever happen. But as this is the fourth consecutive post in which I ask this, I'll leave it at this if it still doesn't get addressed.

Thanks,
Harald

As above, GR says this question is wrongly formulated - there is no preferred definition of global earth coordinates. There are at least two common global coordinates that answer this question - each differently. SC coordinates don't answer it for the trivial reason they don't cover enough of spacetime. (Note: SC coordinates provide two separate coordinate patches, one for interior region, one for exterior. If you want a simultaneity convention between spacetime regions, you need a single coordinate patch that includes both regions. Thus SC coordinates are simply inadmissable for answering your question).

[EDIT: Perhaps this coordinate free description will help ... or not; we'll see. You can't treat causally connected events as simultaneous. The relations of backward and forward going light cones defines the causal structure of spacetime. In the SC geometry, every event outside the EH is in the causal past of a set of events inside the EH. The causal future of any internal event includes only internal events. For a given event, anywhere, you can choose to consider any event between its past and future light cones as simultaneous with it. For an outside event, this means there are a set of interior events in its future light cone that cannot be considered simultaneous. Any interior event 'before' this future light cone can be considered simultaneous with the chosen external event. Thus not only is it possible to choose interior events simultaneous with external event, there are infinite possible choices. Similarly, given an internal event, there is a set of external events in its past light cone; any external event outside of this past light cone is a possible choice for a simultaneous external event]

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PAllen
But as this is the fourth consecutive post in which I ask this, I'll leave it at this if it still doesn't get addressed.

Thanks,
Harald

Just FYI: I feel I and others have have answered all of these questions multiple times in multiple ways, in multiple threads. It seems to me you simply reject the answers but are not willing to say, straight out, that you reject GR.

pervect
Staff Emeritus
OK... that I understand. Now, the Huygens method is non-local, as pictured from a distant frame far in space. So, I guess that my question boils down to asking how to transform that description into a description based on such a non-local frame.

I don't have any idea what you're asking for here either.

Space time is curved, like the surface of the Earth. You can make maps of it, like you can make maps of the Earth's surface. But they won't / can't be to scale except for small regions (frames). The metric describes how the particular part of the map is distorted. To oversimplify greatly, the closer the metric is to unity, the less the distortion.

(I only read the first half)

Considering that Hamilton spends a good part of his time describing a journey into a black hole, (complete with visuals), do you really think it's an accurate reading of him to say that he supports your "time stops at the event horizon, so we dont have to worry about what comes after" idea?

(That was semi-rhetorica., I can say that I certainly don't, and I would be surprised if you did if you thought about it a bit more. Though I've been surprised in this manner before, alas.)

[..] There is a good discussion about spacetime geometry inside a black hole here:
http://www.jimhaldenwang.com/black_hole.htm

In summary here is what you get inside a black hole horizon....all the way to the singularity at the center of the BH [..]
Interesting summary! I had not seen that post which you wrote simultaneously to me.

In particular, by chance (because you did not directly respond to me) it gives an answer from the "distant" perspective that I asked for:

"In the subsequent analysis, we will often consider the perspective of an observer who is at rest at "infinity," that is, very far away from the black hole."

Thanks!

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PAllen
Interesting summary! I had not seen that post which you wrote simultaneously to me.

In particular, by chance (because you did not directly respond to me) it gives an answer from the "distant" perspective that I asked for:

"In the subsequent analysis, we will often consider the perspective of an observer who is at rest at "infinity," that is, very far away from the black hole."

Thanks!

This article looks pretty good, but there is at least one historical blunder. Lemaitre fully resolved the SC coordinate singularity in 1932 with his Lemaitre coordinates. Bergmann's 1942 textbook (I have a copy) already refers to resolution of this 'problem' using a slightly later approach by Robertson (of Robertson-Walker fame). So, at the University textbook level, the problem was considered solved by 1942.

What occurred in 1950 was the first hint that the SC geometry can by geodesically completed into a two world sheet geometry connected by a wormhole bridge; and that the eternal black hole is completed into a prior eternal white hole. None of these geoemetric features apply to a BH that arises from collapse matter - they only apply to the mathematical eternal BH. This effort, begun by J.L. Synge in 1950, reached fruition in the work of Martin Kruskal and George Szekeres, in 1960.

To me, a detector (which follows a world line) is the only thing that can observe.
I fully agree with that; I had no idea that with "worldline" you meant "detector"!
Coordinate labels and simultaneity are abstractions, not observables. So any detector that can observe light emitted inside the EH observes red or blueshift following normal GR rules. The general GR rule is to parallel transport the emitter 4-velociy to the receiver world line along the light path followed. Then express the transported emitter 4 velocity and local light path tangent vector in the local frame basis of the reception event, and use SR doppler formula. This formulation covers every combination of kinematic and curvature and cosmological contribution to redshift in one general method. [..]
2) You can't even write an alternative equivalent formula for inside the horizon because the region inside the horizon is not static, so there is no such thing, even approximately, of a gravitational potential. The concept of gravitational redhsift factored out separately from general redshift as I described above is possible only for static spacetime. [..] the light path goes from a static region of spacetime to a non-static region. [..]
Short answer: your question reflects fundamental misunderstanding of GR; corrected in the only way I know, your conclusion is wrong.
Thanks - Regretfully I am not familiar with "non-static spacetime" but perhaps that Naty's link that clarifies.
Perhaps this coordinate free description will help ... or not; we'll see. [..] not only is it possible to choose interior events simultaneous with external event, there are infinite possible choices. Similarly, given an internal event, there is a set of external events in its past light cone; any external event outside of this past light cone is a possible choice for a simultaneous external event]
It doesn't help yet; does it correspond to the "swapping of space and time"?
Just FYI: I feel I and others have have answered all of these questions multiple times in multiple ways, in multiple threads. It seems to me you simply reject the answers but are not willing to say, straight out, that you reject GR.
I don't know why you would think that (except for 1916GR which is subtly rejected by mainstream). Your answer implies that those questions have no answer; however several web links seem to give an answer.
I don't have any idea what you're asking for here either.
Space time is curved, like the surface of the Earth. You can make maps of it, like you can make maps of the Earth's surface. But they won't / can't be to scale except for small regions (frames). The metric describes how the particular part of the map is distorted. To oversimplify greatly, the closer the metric is to unity, the less the distortion.
I asked for a "distant perspective" which is now found to be given in several links.
Considering that Hamilton spends a good part of his time describing a journey into a black hole, (complete with visuals), do you really think it's an accurate reading of him to say that he supports your "time stops at the event horizon, so we dont have to worry about what comes after" idea?

(That was semi-rhetorica., I can say that I certainly don't, and I would be surprised if you did if you thought about it a bit more. Though I've been surprised in this manner before, alas.)
Surprise for me - and perhaps also for you:
I now found that Hamilton also discusses this question, and answers it with a falling space/flowing river model - a kind of ether inflow (question 9):

I thought that the "falling space" model was disproved, but this is apparently not established:
- "ajp.aapt.org/resource/1/ajpias/v76/i6/p519_s1?" [Broken]

Anyway, GR is based on a model of static space with "curvature" due to "fields". "flowing" space is fundamentally different from "curved" space; it is conceptually more different from GR than LET from SR. Einstein's light bending calculation method according to which light locally slows down doesn't even apply to flowing space! With that model time does not stop at the event horizon. Perhaps flowing space gives the same verifiable predictions as GR, but it is definitely not the same model as the one Einstein used for GR and to which I referred with my question; now reading the interesting link by Naty.

PS. Links to two opinions, not including falling space theory:
http://arxiv.org/abs/gr-qc/0609024 (found by me, discussed in Discovermagazine)
http://www.jimhaldenwang.com/black_hole.htm (found by Naty)

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PAllen
Thanks - Regretfully I am not familiar with "non-static spacetime" but perhaps that Naty's link that clarifies.
Yes, the link Nat attempts to provide intuitive explanation of the non-static spacetime of the BH interior. Generally, the concept of static is simply: Can you find a way to introduce a family of timelike world lines covering spacetime (congruence, in the technical terminology), such that the metric does not change along each of these. More precisely, can you find a timelike killing field. If you can, then you can introduce coordinates of the familiar type (one timelike, 3 spacelike) such that the metric components are not a function of the time coordinate.

For a non-static spacetime, the above is impossible. This means it becomes impossible to do any of the following:

- model gravity by a potential (a function of position)
- factor redshift into gravitiational and kinemetic in any meaningful way. You can compute redhift between an emitter and detector whose world lines you specify, but can't factor it into separate components, as you can in a static spacetime.
It doesn't help yet; does it correspond to the "swapping of space and time"?
The swapping of space and time is coordinate artifact of SC coordinates. It does not happen in Lemaitre or Kruskal coordinates. What is an invariant feature of causal structure of the interior versus exterior of a BH event horizon is that the future pointing light cone of all interior events includes no exterior events. Further, for the simple, non-spinning, spherical BH, the future pointing light cone of every interior event includes the singularity; and every timelike world line ends at the singularity.
I don't know why you would think that (except for 1916GR which is subtly rejected by mainstream). Your answer implies that those questions have no answer; however several web links seem to give an answer.
On the contrary, I thought I provided multiple answer, and continue to be frustrated that you claim otherwise. I said, briefly:

- there is no such thing as global frames in GR, only gl0bal coordinates; and there isn't a way to strongly favor one over another as there is for global inertial frames in SR. However, I then describe 2 specific ways, and also the general rule, for establishing simultaneity between exterior and interior events.
I asked for a "distant perspective" which is now found to be given in several links.
I gave you two specific ones and also a general rule.
Surprise for me - and perhaps also for you:
I now found that Hamilton also discusses this question, and answers it with a falling space/flowing river model - a kind of ether inflow (question 9):
No surprise at all. I didn't think this was necessary to resolve your questions. If it is helpful, great.
I thought that the "falling space" model was disproved, but this is apparently not established:
- "ajp.aapt.org/resource/1/ajpias/v76/i6/p519_s1?" [Broken]

Anyway, GR is based on a model of static space with "curvature" due to "fields".
This is wrong. It is based on curvature of spacetime. Static solutions arise for artificial special cases (one non-spinning object in the universe). As with any other theory, ideal, special case, solutions can be useful approximations to more realistic scenarios (e.g only one massive body in a region; rotation not extreme,). But, as with any theory, you need to know the limits of applicability of ideal solutions.
"flowing" space is fundamentally different from "curved" space;
Flowing space is just an intuitive model of curved spacetime that cannot be treated as static.
it is conceptually more different from GR than LET from SR.
Wrong, it is a direct consequence of the equations Einstein and Hilbert wrote down in 1916. Nothing has been added to or changed about those equations or the definition of observables. Mathematical technique has evolved. Understanding of what the equations imply has evolved - Einstein was involved in plenty of it, through the 1940. Some of Einstein's philosophic understandings of GR are not so widely shared now, but this has no bearing on physical predictions.
Einstein's light bending calculation method according to which light locally slows down doesn't even apply to flowing space! With that model time does not stop at the event horizon.
Einstein was simply doing a calculation for the simplest static case (sun considered effectively motionless and isolated; a very good approximation). Are you interpreting one special case computation as the whole theory??!!
Perhaps flowing space gives the same verifiable predictions as GR, but it is definitely not the same model as the one Einstein used for GR and to which I referred with my question; now reading the interesting link by Naty.
Again, flowing space is just one intuitive description of spacetime curvature without a timelike killing vector, so it cannot be treated as a static geometry. Note that even a static spacetime has curvature of time as well as space. It is just that that the curvature can be considered not to evolve in time.

[edit: The SC exterior static geometry is to GR (and the EFE) as the coulomb field of a single charge is to the richness of Maxwell's theory. ]

[Edit: I see that Hamilton has a very specific concept of flowing space, that he applies even to static regions. This is different from a more generic concept I was using only for non-static regions. However, it is crucial to note that Hamilton is just providing an interpretational model. It adds nothing, changes nothing, about GR. It is just an approach to picturing some of its consequences. One cannot speak about its being right or wrong; only useful or not-useful for your own understanding.

Note that this link Harrylin gave:

http://arxiv.org/abs/gr-qc/0609024

is not discussing classical GR at all. It is discussing one group's conclusions about how quantum corrections would modify GR (in the absence of any accepted theory of quantum gravity). ]

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In general light is not fast enough to escape the gravity of a black hole. But as stated many times, when you are dealing in black holes the laws on Physics seem to be broken. However I guess if you could bend space time enough around the center of the SMB light could possibly escape the intense gravity.

In general light is not fast enough to escape the gravity of a black hole. But as stated many times, when you are dealing in black holes the laws on Physics seem to be broken. However I guess if you could bend space time enough around the center of the SMB light could possibly escape the intense gravity.

What evidence do you have of this? Light can't even orbit too close to the event horizon--there is a separate horizon composed of nothing but photons orbiting further out from the event horizon. And any photons falling in closer will have their worldlines pointing to the center. The event horizon itself is the point past which even a photon pointed directly away from the singularity would have no hope of escaping. In other words, the point past which all worldlines curve back towards the center.

Besides, the current theories only break down at the singularity, which is well past the "point of no return". The physics up to that point is pretty solid (to use an admittedly horrendous pun).

"Bending space time enough" is just going to make the gravitational effect all the more intense, because an inertial path taken through space time is determined by a geodesic--the shortest path taken through curved manifold (in this case, spacetime.) and "bending space time" is just going to increase the curvature of the geodesics.

Yes, the link Nat attempts to provide intuitive explanation of the non-static spacetime of the BH interior. Generally, the concept of static is simply: Can you [..] introduce coordinates of the familiar type (one timelike, 3 spacelike) such that the metric components are not a function of the time coordinate.

For a non-static spacetime, the above is impossible. This means it becomes impossible to [..]
- factor redshift into gravitiational and kinemetic in any meaningful way. You can compute redhift between an emitter and detector whose world lines you specify, but can't factor it into separate components, as you can in a static spacetime.
[..]
The swapping of space and time is coordinate artifact of SC coordinates. It does not happen in Lemaitre or Kruskal coordinates.
Thanks - that's clearer - and better than rotating a clock into a ruler. :tongue2: Anyway it appears that that reference is not peer reviewed.
[..] On the contrary, I thought I provided multiple answer [..] I gave you two specific ones and also a general rule.
I saw that you gave the names of two methods that can be used to give different answers...
[rearranging:] [..] Flowing space is just an intuitive model of curved spacetime that cannot be treated as static. [Edit: I see that [..] applies even to static regions. [..]
Good! - that is exactly my point. I will start a topic on that model vs Einstein's GR.
Note that this link Harrylin gave:

http://arxiv.org/abs/gr-qc/0609024

is not discussing classical GR at all. It is discussing one group's conclusions about how quantum corrections would modify GR (in the absence of any accepted theory of quantum gravity). ]
Good try to discredit it (and already your second attempt, as it's what discovermagazine discussed) - but untrue according to Physical Review. The "analysis is in 3+1 dimensions and within conventional general relativity."

It provides perhaps the clearest and most up-to-date answer to the question of this thread, and from a quality source.
[edit: it has 28 citations, so there may be a more relevant newer article on this]

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PAllen
Good try to discredit it (and already your second attempt, as it's what discovermagazine discussed) - but untrue according to Physical Review. The "analysis is in 3+1 dimensions and within conventional general relativity."

It provides perhaps the clearest and most up-to-date answer to the question of this thread, and from a quality source.
[edit: it has 28 citations, so there may be a more relevant newer article on this]

Here is its abstract:

"We study the formation of black holes by spherical domain wall collapse as seen by an asymptotic observer, using the functional Schrodinger formalism. To explore what signals such observers will see, we study radiation of a scalar quantum field in the collapsing domain wall background. The total energy flux radiated diverges when backreaction of the radiation on the collapsing wall is ignored, and the domain wall is seen by the asymptotic observer to evaporate by non-thermal pre-Hawking radiation'' during the collapse process. Evaporation by pre-Hawking radiation implies that an asymptotic observer can never lose objects down a black hole. Together with the non-thermal nature of the radiation, this may resolve the black hole information loss problem. "

Hawking radiatiion and pre-Hawking radiation are outside of classical GR. I have read enough to see the obvious fact that every aspect of its conclusions is based on quantum corrections to GR. Even the topic: "Information Loss" is a problem that exists only for quantum mechanics + GR. Evaporation is not part of classical GR, and is fundamental to their argument. This paper is not a paper on classical GR at all.

PAllen
Good! - that is exactly my point. I will start a topic on that model vs Einstein's GR.

Do you consider spacetime diagrams or the block universe different theories than SR? To me, they are just different approaches to picturing SR. Hamilton's river model's are not a new theory, just a conceptual aid. They change not a single equation or rule for computing an observable.

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PAllen
I saw that you gave the names of two methods that can be used to give different answers...

Thus answering the question at hand, which was "is there a way to say what event for a distant observer is simultaneous with reception of a signal by an interior observer?" The answer being: two well known possible conventions; plus the applicability of the general SR/GR rule that indicates there are infinite admissable answers and no way to say one is 'right'. If you want more specifics, pose a specific scenario with numbers, and I will try to compute a specific answer for you, using one or both specific conventions.

OK, I now read sufficiently of http://arxiv.org/abs/gr-qc/0609024 to give a quick summary as concerns the topic here.

"Our analysis is in 3+1 dimensions and within conventional general relativity. [..] we find that Schwarzschild coordinates are sufficient to answer the very specific set of questions we ask from the asymptotic observer’s viewpoint."

"the standard result [is] that the formation of an event horizon takes an infinite (Schwarzschild) time if we consider classical collapse."

And they conclude:

"First, we studied the collapse of a gravitating spherical domain in [..] classical [..] theory, ignoring any evaporative processes. [...] our results show that [..] the horizon does not form in a finite time".

This is, as I mentioned earlier, also discussed on another forum:

A follow-up paper states and explains the same, perhaps even more clearly:

"Black Hole - Never Forms, or Never Evaporates" (title)
- http://arxiv.org/abs/1102.2609

From that I conclude that the modern answer to the question of this thread is that according to GR it can never happen - similar to "what happens when I go faster than light".

I'm satisfied with that answer (and note that the original poster did not come back to this thread).

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[..] If you want more specifics, pose a specific scenario with numbers, and I will try to compute a specific answer for you, using one or both specific conventions.
Thanks for your kind offer; but it won't be needed!

PS. I started the new topic on "flowing space models" here:

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PAllen
First, one author does not represent the 'modern view'. Krauss is recognized as a cosmologist not a GR expert. Even so, I show how I believe you are over-interpreting the claims of this paper.

OK, I now read sufficiently of http://arxiv.org/abs/gr-qc/0609024 to give a quick summary as concerns the topic here.

"Our analysis is in 3+1 dimensions and within conventional general relativity. [..] we find that Schwarzschild coordinates are sufficient to answer the very specific set of questions we ask from the asymptotic observer’s viewpoint."
Yes, a specific set of questions. There is never any dispute about what light or radiation reaches a distant observer from the BH region.

The different question that came up in this thread was: can the distant observer send a message to an infaller? Where is the infaller when the message reaches them? Is there a way to talk about 'when' for the external observer the infaller gets the message? In classical GR, the first two of these are physical observables with absolutely indisputable answers; the last is purely a matter of convention - true for any question about distant simultaneity. The indisputable answer to the physical question:

- the infaller will receive signals from the distant observer at a well defined finite time on their watch.
- the infaller will continue receiving such signals past the EH all the way to the singularity.

This paper simply chose not address these question, so in no way does it refute them.
"the standard result [is] that the formation of an event horizon takes an infinite (Schwarzschild) time if we consider classical collapse."
Schwarzschild time is not an observable of GR, it is a coordinate quantity. The only relevent observable for classical GR is the never disputed observation that no signal or influence will propagate from the EH or inside to a distant observer.
And they conclude:

"First, we studied the collapse of a gravitating spherical domain in [..] classical [..] theory, ignoring any evaporative processes. [...] our results show that [..] the horizon does not form in a finite time".
Now this I would say is wrong without qualification. The question is whose time? If you follow an infalling dust particle in a collapse, the horizon forms in finite time, the particle crosses it. Further, the area of the externally observed, ultra-redshift boundary grows as new matter falls into the region. Each new piece of matter you follow in its local frame crosses a larger surface area horizon.

So here, this phrasing (at least the snippet you've given, taken in isolation) is at least misleading. It certainly does not represent consensus view of classical GR.
This is, as I mentioned earlier, also discussed on another forum:

A follow-up paper states and explains the same, perhaps even more clearly:

"Black Hole - Never Forms, or Never Evaporates" (title)
- http://arxiv.org/abs/1102.2609

"it shows that so long as the mechanism of black hole evaporation satisfies a quite loose condition that the evaporation lifespan is finite for external observers, regardless of the detailed mechanism and process of evaporation, the conundrums above can be naturally avoided.'

Evaporation is outside the scope of classical GR.
From that I conclude that the modern answer to the question of this thread is that according to GR it can never happen - similar to "what happens when I go faster than light".

I'm satisfied with that answer (and note that the original poster did not come back to this thread).

First, one author does not represent the 'modern view'. Krauss is recognized as a cosmologist not a GR expert.
I used the pragmatic Wikipedia method: check out the citations over 4 years.

Even so, I show how I believe you are over-interpreting the claims of this paper.
[..] The different question that came up in this thread was: can the distant observer send a message to an infaller? Where is the infaller when the message reaches them? Is there a way to talk about 'when' for the external observer the infaller gets the message?
Instead I only referred to the topic as in the title question of this thread.

Now this I would say is wrong without qualification. The question is whose time? [..]
That is specified: "the asymptotic observer" - which corresponds to the time I referred to in the 10 foregoing posts. They elaborate: "More concretely, if a black hole is formed in the Large Hadron Collider, it has to be observed by physicists sitting on the CERN campus."

This is how the more recent paper by Yi phrases the same (and with that I'll leave this thread):

"According to Oppenheimer & Snyder [7], there are two influencing conclusions of black hole(BH) formation: “[..] an external observer sees the star asymptotically shrinking to its gravitational radius”. It must be mentioned that the word “see” means measuring by coordinates, not “watching” the light emitted from the star".

PAllen
I used the pragmatic Wikipedia method: check out the citations over 4 years.
Counting citations without looking at the goals and content of the papers doesn't mean much. Here is later summary by a universally recognized GR expert on these issues at the boundary of classical and quantum gravity (it cites this paper and many others):

http://arxiv.org/pdf/0901.4365v3.pdf

I note the following, which I view as the continuing, unchanged, majority consensus for classical GR:

Classical general relativist: Eternal black holes certainly exist mathematically, as stationary
vacuum solutions to the Einstein equations. (See, for example, [10, 11, 12, 13], or any of the
many standard textbooks in general relativity [14].) Furthermore classical astrophysical black holes
(future event horizons) certainly exist mathematically as the end result of classical collapse based
on certain physically plausible equations of state. (See, for example, [15].)
That is specified: "the asymptotic observer" - which corresponds to the time I referred to in the 10 foregoing posts. They elaborate: "More concretely, if a black hole is formed in the Large Hadron Collider, it has to be observed by physicists sitting on the CERN campus."
Since a defining feature of such micro-black holes is quantum behavior, this is ipso facto completely outside of classical GR.
This is how the more recent paper by Yi phrases the same (and with that I'll leave this thread):

"According to Oppenheimer & Snyder [7], there are two influencing conclusions of black hole(BH) formation: “[..] an external observer sees the star asymptotically shrinking to its gravitational radius”. It must be mentioned that the word “see” means measuring by coordinates, not “watching” the light emitted from the star".

"Measuring coordinates" is nonsense. Coordinates are not observable, in SR or GR. Further, IMO, the introduction to the Yi paper announces him as crank (unlike Krauss et.al., who make no equivalent statements). Schwarzschild time, per se, is not an observable for anyone. All you can talk about is light and signals received by some observer, at various proper times along their world line. Coordinates are computed quantities, defined for various purposes.

A geometric translation of "SC time becomes infinite as an infall trajectory approaches the horizon" is:

If I compute simultaneity using one particular set of spacelike-hypersurfaces (distant simultaneity itself being inherently unsobservable), then I never find an event on an external observer's world line to be simultaneous with an infaller crossing the horizon.

However, if I make any of an inifnite number of different choices for simultaneity surfaces, I can declare which external event I compute to be simultaneous with an EH crossing event for an infaller.

[..] Here is later summary by a universally recognized GR expert on these issues at the boundary of classical and quantum gravity (it cites this paper and many others):

http://arxiv.org/pdf/0901.4365v3.pdf

[..]
Popped in for one last look at this thread, and see there: Nice - I had missed that one!
I see that that expert imagines general relativists to be mathematicians: "exist mathematically" isn't physical existence.

Thanks again,
Harald

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PAllen
Popped in for one last look at this thread, and see there: Nice - I had missed that one!
I see that that expert imagines general relativists to be mathematicians: "exist mathematically" isn't physical existence.

Thanks again,
Harald

Well part of this is that nearly everyone, myself included, think the universe is quantum in nature; thus GR pushed to extreme regimes is unlikely to be correct. I simply clearly separate this not-yet understood realm, from classical GR. In EM, we have little difficulty saying: according to Maxwell's equations, xyz happens (e.g a stable atom cannot exist); accounting form quantum theory, it can. Similarly, I believe (almost certainly) that (due to quantum corrections):

- singularities don't actually exist in our universe
- compact objects (collapsed stars; active galactic centers) share many broad properties, observed from a distance, as classical event horizons; however, the details are likely different. How different, I don't know. For example, the question of whether BH horizons produce 'firewalls' is currently being debated between Polchinksi and Susskind (both prominent string theorists).

pervect
Staff Emeritus
Observation of Incipient Black Holes and the Information Loss Problem
Tanmay Vachaspati, Dejan Stojkovic, Lawrence M. Krauss
(Submitted on 7 Sep 2006 (v1), last revised 7 Jun 2007 (this version, v3))

We study the formation of black holes by spherical domain wall collapse as seen by an asymptotic observer, using the functional Schrodinger formalism. T

"functional Schrodinger formalism", whatever else it may be is NOT classical.

While I'm not particulary fond of at least one of the authors (Krauss, as in my opinion he messed the"Physics of StarTrek" with some quirky popularizations) the paper probably deserves some serious study. But it is no sense about CLASSICAL black holes.

(And I'm sorry, but I can't really address the non-classical aspects of the paper due to a lack of familiarity. Perhaps someone else can. But I feel quite comfortable with talking about the CLASSICAL theory of black holes.)

One thing I think should be pretty clear. The paper will NOT answer the experiences of someone who falls into a black hole. Which is really the question under discussion - and not at all related to the topic of the paper. At least I thought that's what the question was. It seems like the topic is morphing around, never a good sign.

From what I gather, you seem to think that someone who falls into a black hole just vanishes or something? And you ignore all the various published papers about what happens inside the event horizon - for reasons that I don't follow. I"m really not sure what you think happens when there is "geodesic incompleteness". Imagine that you drew a space-time diagram, and you came to the edge of the paper, and you just stopped drawing the worldline. That is an informal description of "geodesic incompletness".

Geodesic incompletenss is NOT a required feature of the event horizon, though you can put it in if you really want to (you could have geodesics vanish somewhere other than the event horizon too - you simply decide where they vanish, and declare that it happens). It's rather like sketching a map of the universe on some piece of paper, and saying that anything that goes "off the map" just vanishes from existence.

You can do it, but it's silly.

I can point out (as I have many times in the past) the analogous situation of someone falling behind the Rindler horizon. The situation provides much insight. While I doubt there are any papers on the topic, there may be a textbook question or two. It's quite easy for the whole Earth to fall behind the Rindler horizon of an acclerating spaceship, and from the spaceship you'll see all the usual reshifting and apparent "freezing" of time, just as you will see with a black hole horizon, or any other event horizon. But, it should be reasonably obvious that nothing that happens on the remote spaceship is going to affect the Earth - if the Earth falls behind the Rindler horizon of the spaceship in 2012, the Earth is not going to vanish from existence, or cease to exist, in any meaningful sense. The spaceship, however, won't be able to see any events subsequent to 2012 as long as it continues to accelerate.