Life below the Schwarzschild radius

[JeroenDeDauw]

Note: I did not study psychics and only have a vague-ish conceptual understanding of stuff

Seems to me one of these points must be wrong:

* One can survive passing into the Schwarzschild radius of a black hole
* The Schwarzschild radius of a black hole (or it's surface?) represents a region of maximum entropy
* Life cannot exist in a region of maximum entropy
* There is a contradiction here so one of the above 3 points is wrong

Which one is it? :)

 

[Dale]

Hi JeroenDeDauw, welcome to PF!

What is a region of maximum entropy? Does entropy even have a maximum?

 

[PAllen]

While within Schwarzschild BH, due to perfect symmetry, all paths followed by matter lead to the singularity, in more realistic black holes there are other possibilities (there is still a singularity, at leased according to classical GR, but not all matter must meet the singularity).

These possibilities are explored in the following amusing, speculative, but scientifically sound paper:

http://arxiv.org/abs/1103.6140

 

[atyy]

I'm not sure. In http://arxiv.org/abs/1207.3123, the hypothesis of black hole complementarity includes

"Postulate 3: To a distant observer, a black hole appears to be a quantum system with discrete energy levels. The dimension of the subspace of states describing a black hole of mass M is the exponential of the Bekenstein entropy S(M)."

"Postulate 4: A freely falling observer experiences nothing out of the ordinary when crossing the horizon."

So perhaps the Bekenstein entropy only applies to the distant observer, and not the one crossing the event horizon? (Incidentally, that paper argues that black hole complementarity is wrong for sufficiently old black holes. I don't believe either complementarity or firewalls are known for sure. What we do know is that black hole's have entropy only if quantum mechanics is taken into account.)

 

[tom.stoer]

The basic question is whether one wants to treat the BH classically or quantum mechanically. For classical BHs there are exact solutions, and for large BHs there is no reason to believe in anything strange happening when crossing the horizon. For quantum mechanical BHs there are speculations regarding quantum effects up to the horizon scale (fuzzball proposal in string theory), black hole firewall etc.; here the problem is that we do not have a fully developped theory of quantum gravity and therefore can't address all questions (quantum effects, gravitational entropy, ...) in all details; so there is still a large amount of speculations.

 

[JeroenDeDauw]

Thanks for the welcome.

> What is a region of maximum entropy? Does entropy even have a maximum?

I have read that when gravity is held into account, then dumping all available matter is the state of highest entropy (as the back hole can only be identified by charge, spin, mass and location, which are very few distinguishable macroscopic states compared to non-observable microscopic states). To increase the entropy, you'd need to add particles so the state space becomes bigger, which just leads to the hole becoming bigger. You can thus not increase the entropy per region of space beyond that of a black hole.

I do have the suspicion the fallacy in my original points is seeing this as a flat region, while the actual entropy (or most of it) is located at the singularity. Anyone think I'm wrong in identifying this as my mistake?

> so there is still a large amount of speculations.

Sure, don't think my particular question requires a theory of quantum gravity to be answered though.

> What we do know is that black hole's have entropy only if quantum mechanics is taken into account.

Heh? How's that? The description I gave above does not depend on quantum mechanics at all AFAICS.

> These possibilities are explored in the following amusing, speculative, but scientifically sound paper

Oh thanks, looks like an interesting read :)

> I'm not sure. In http://arxiv.org/abs/1207.3123, the hypothesis of black hole complementarity includes

Thanks for that as well. Never heard of black hole firewalls, so will see if I can understand that paper without looking at the man page of iptables.

 

[harrylin]

Note: I did not study psychics and only have a vague-ish conceptual understanding of stuff

Seems to me one of these points must be wrong:

* One can survive passing into the Schwarzschild radius of a black hole
* The Schwarzschild radius of a black hole (or it's surface?) represents a region of maximum entropy
* Life cannot exist in a region of maximum entropy
* There is a contradiction here so one of the above 3 points is wrong

Which one is it? :)

Hi Jeroen,

Concerning the first point, several new papers (and also several old papers) imply that life cannot not happen there - however the arguments had nothing obvious to do with entropy. See the recent discussion in this forum, as well as the linked discussion in another forum:
https://www.physicsforums.com/showthread.php?p=4129133

 

[PAllen]

Hi Jeroen,

Concerning the first point, several new papers (and also several old papers) imply that life cannot not happen there - however the arguments had nothing obvious to do with entropy. See the recent discussion in this forum, as well as the linked discussion in another forum:
https://www.physicsforums.com/showthread.php?p=4129133

I need to respond that in the opinion of many on on these forums, harrylin misinterprets both sources linked. The first one linked says:

"This time dilation factor tends to zero as r approaches the Schwarzschild radius rs, which means that someone at the Schwarzschild radius will appear to freeze to a stop, as seen by anyone outside the Schwarzschild radius. "

The key phrase is highlighted. The accepted interpretation is that this says nothing about the experience of the infaller themselves - it is just a consequence the effect of extreme intervening net curvature on light rays or other signals.

As for the other paper lined in that post (the paper, not the discovery magazine summary), other people here who looked at the paper view it as saying nothing at all new or different about black holes intertpreted via classical GR; it makes claims about rate of collapse versus evaporation (a purely quantum phenomenon). This result is considered one among many speculative proposals for quantum corrrection; it is not considered consensus. For example, the following paper by quantum gravity expert argues that all major conclusions of the paper behind the Discover article are wrong:

http://arxiv.org/abs/0906.1768

(but this is also just another ongoing contribution to a debate that will not be settled until there is a consensus quantum theory of gravity that can make reliable predictions).

 

[harrylin]

I need to respond that in the opinion of many on on these forums, harrylin misinterprets both sources linked. [..]

There was no need for that at all: the PF discussion which I made sure to be visible in the link includes a lot of arguments from a certain PAllen as well as others - that should suffice for Jeroen to form his own opinion. However it seems that PAllen tries to prevent that Jeroen reads about that other discussion and the paper that it relates to.

He should read it for themselves instead of listening to him or me. The other discussion (on discovermagazine http://blogs.discovermagazine.com/badastronomy/2007/06/19/news-do-black-holes-really-exist/) was about Phys.Rev.D76:024005,2007 and for this forum part III, "CLASSICAL TREATMENT OF DOMAIN WALL COLLAPSE" (the non-QM part) is relevant. It is also on Arxiv: http://arxiv.org/abs/gr-qc/0609024

 

[PAllen]

He should read it for themselves instead of listening to him or me. The other discussion (on discovermagazine http://blogs.discovermagazine.com/badastronomy/2007/06/19/news-do-black-holes-really-exist/) was about Phys.Rev.D76:024005,2007 and for this forum part III, "CLASSICAL TREATMENT OF DOMAIN WALL COLLAPSE" (the non-QM part) is relevant. It is also on Arxiv: http://arxiv.org/abs/gr-qc/0609024

Yes, that is a key section to read, also in context to the framework set in the introduction. Some key conclusions in this section:

"This solution implies that,
from the classical point of view, the asymptotic observer
never sees the formation of the horizon of the black hole,
since R(t) = RS only as t → ∞."

and from the introduction, setting the relation of this work to other work:

"We emphasize
that all our discussion, unless explicitly stated,
refers to the Schwarzschild time, t, and this defines the
time slicing of the spacetime. As is well known, the
Schwarzschild coordinate system breaks down at a black
hole horizon, and there is danger that our analysis will
also break down at some point during the gravitational
collapse. However, we do not encounter any such difficulties,
suggesting that our calculation is self-consistent."

I believe the last sentence is specifically referring to the quantum analysis, since they never attempt to ask the question of collapse for a shell observer, classically. The main purpose of the paper is to argue that that when corrected for evaporation, they don't need to ask that question.

 

[atyy]

> What we do know is that black hole's have entropy only if quantum mechanics is taken into account.

Heh? How's that? The description I gave above does not depend on quantum mechanics at all AFAICS.

The temperature of a black hole in classical general relativity is absolute zero. Bekenstein argued that a black hole must have a temperature because of thermodynamics - but that contradicts classical general relativity. Hawking then showed that if one makes a "semiclassical" calculation, an approximation in which matter is quantized on a fixed curved spacetime, then black holes give off thermal radiation - justifying Bekenstein's argument. This is why black hole entropy depends on quantum mechanics. Because of Bekenstein and Hawking's work, the formula for black hole entropy is called the Bekenstein-Hawking entropy.

Take a look at section 4.1 of http://arxiv.org/abs/gr-qc/9912119 for the argument that classical black holes are at absolute zero.

 

[harrylin]

[..] [..] if one makes[..] an approximation in which matter is quantized on a fixed curved spacetime, then black holes give off thermal radiation [..]. This is why black hole entropy depends on quantum mechanics. [..]

Then this topic belongs in the General Physics forum. Can it be moved?

 

[harrylin]

Yes, that is a key section to read, also in context to the framework set in the introduction. Some key conclusions in this section:

"This solution implies that,
from the classical point of view, the asymptotic observer
never sees the formation of the horizon of the black hole,
since R(t) = RS only as t → ∞."

Your bold face is misleading: they do not confound coordinate time with the time that information is received.
At the end of that section they clarify:

"In our case
there is no pre-existing horizon, which is itself taking an
infinite amount of time to form during collapse."

And next in the discussion:

"First, we studied the collapse of a gravitating spher-
ical domain in both classical and quantum theory, ig-
noring any evaporative processes. It has been suggested
in the literature that quantum fluctuations can cause
the collapse and formation of a black hole in a finite
(Schwarzschild) time [3]. However, our results show that
this is not the case and the horizon does not form in a
finite time even in the full quantum treatment." (bold face mine)

 

[PAllen]

Your bold face is misleading: they do not confound coordinate time with the time that information is received.
At the end of that section they clarify:

"In our case
there is no pre-existing horizon, which is itself taking an
infinite amount of time to form during collapse."

And next in the discussion:

"First, we studied the collapse of a gravitating spher-
ical domain in both classical and quantum theory, ig-
noring any evaporative processes. It has been suggested
in the literature that quantum fluctuations can cause
the collapse and formation of a black hole in a finite
(Schwarzschild) time [3]. However, our results show that
this is not the case and the horizon does not form in a
finite time even in the full quantum treatment." (bold face mine)

You are still mis-interpreting this.

Re first paragraph: No pre-existing horizon is characteristic of any collapse scenario. Clasically, 'infinite time to form' is valid description of distant perception due to infinite aging of light signals. Papers are written in the context of established expert understanding. The full details are not repeated unless disputed. Nothing here is disputing any aspect of classical understanding. The intro makes clear they are aware of the limitations of SC time classically. A key point is that their math for the classical case is identical to standard treatments.

The second paragraph is describing what is new, and is all quantum in context: they argue that, contrary to some earlier treatments, quantum corrections cause the horizon never to form at all. The word 'even' is contrasting their quantum result to earlier conclusions that quantum affects exacerbated the classical dichotomy in causation. Again, the math is the key: their formulas in the quantum sections are genuinely different than those prior investigators arrived at.

Finally, it is important to realize this is one contribution to a long, continuing debate. The literature contains a long, unanswered, refutation of this paper by a representative of that prior consensus, re-arguing at length the prior consensus that quantum effects do not prevent horizon formation.

 

[stevendaryl]

Hi Jeroen,

Concerning the first point, several new papers (and also several old papers) imply that life cannot not happen there - however the arguments had nothing obvious to do with entropy. See the recent discussion in this forum, as well as the linked discussion in another forum:
https://www.physicsforums.com/showthread.php?p=4129133

I don't think that can possibly be correct. Here's a counter-argument: Suppose you have a spherical shell of matter. You place explosives symmetrically all around the shell and cause it to implode. If the mass of the incoming shell is great enough, a black hole will be formed.

But people living at the center of the shell will not notice anything at all until the light from the explosions reaches them. So there will be a period in which life will go on as normal inside the black hole.

 

[harrylin]

You are still mis-interpreting this.

Re first paragraph: No pre-existing horizon is characteristic of any collapse scenario. Clasically, 'infinite time to form' is valid description of distant perception due to infinite aging of light signals. Papers are written in the context of established expert understanding. [..] Nothing here is disputing any aspect of classical understanding. [..]

(red face mine)
You express a fundamental misunderstanding of what the authors meant, as you try to interpret it as meaning nothing controversial. Perhaps this explanation by one of them will help:

"what is controversial about the new finding is that "from an external viewer's point it takes an infinite amount of time to form an event horizon and that the clock for the objects falling into the black hole appears to slow down to zero," said Krauss, director of Case's Center for Education and Research in Cosmology."
http://www.sciencedaily.com/releases/2007/06/070620115358.htm
Or, better, from their own press department "Black holes don't exist, Case physicists report":
http://blog.case.edu/case-news/2007/06/20/blackholes
I suggest to ask Susan Griffith if you still don't believe it.

Finally, it is important to realize this is one contribution to a long, continuing debate. The literature contains a long, unanswered, refutation of this paper by a representative of that prior consensus, re-arguing at length the prior consensus that quantum effects do not prevent horizon formation.

The issue is not horizon formation, but horizon completion in finite time. But it is good to see you admit that there is no consensus on this. I gave the OP a possible solution to his question; for him to decide if it is helpful.

 

[harrylin]

I don't think that can possibly be correct. Here's a counter-argument: Suppose you have a spherical shell of matter. You place explosives symmetrically all around the shell and cause it to implode. If the mass of the incoming shell is great enough, a black hole will be formed.

But people living at the center of the shell will not notice anything at all until the light from the explosions reaches them. So there will be a period in which life will go on as normal inside the black hole.

Just as long ago in 1939, the discussion is about the forming of the black hole and how that affects matter outside. But you give a very interesting scenario, questioning what happens on the inside. I have an idea, but I must think about it and my suggestion can only be that of an amateur. Alternatively, you could also present it to the authors

ADDENDUM: finally it didn't take long for me to come up with an amateur solution of your paradox. In their models the "black hole" condition is a limit state that is never reached. Thus I think that people living at the centre of the shell will indeed live on rather normally at first, until they are smashed by the great g forces and things like that. Before that moment they may perceive what looks like an accelerating universe around them.

 

[PAllen]

(red face mine)
You express a fundamental misunderstanding of what the authors meant, as you try to interpret it as meaning nothing controversial. Perhaps this explanation by one of them will help:

"what is controversial about the new finding is that "from an external viewer's point it takes an infinite amount of time to form an event horizon and that the clock for the objects falling into the black hole appears to slow down to zero," said Krauss, director of Case's Center for Education and Research in Cosmology."
http://www.sciencedaily.com/releases/2007/06/070620115358.htm
Or, better, from their own press department "Black holes don't exist, Case physicists report":
http://blog.case.edu/case-news/2007/06/20/blackholes
I suggest to ask Susan Griffith if you still don't believe it.

An infalling clock appearing to slow down per an external observer is not controversial but universally accepted.

I read these things and see all the 'new' statements as being clearly quantum in nature because they refer to pre-hawking or hawking radiation and evaporation, none of which occur classically.

Note, also, that papers disagreeing with it view it as saying nothing new classically; they don't comment on that part because it is all identical to established results. The controversy is over the new claim: that the competition between evaporation and collapse is won by evaporation.

The page by Susan Griffith looks 100% quantum in its description to me.

The issue is not horizon formation, but horizon completion in finite time. But it is good to see you admit that there is no consensus on this. I gave the OP a possible solution to his question; for him to decide if it is helpful.

It is wide open in with quantum effects considered. It is not open classically.

 

[harrylin]

An infalling clock appearing to slow down per an external observer is not controversial but universally accepted. [..] The controversy is over the new claim: that the competition between evaporation and collapse is won by evaporation. [..]

Of course that can't be what he means, and it contradicts what he said, but you insist that it is what he means. Thus in the end you cannot avoid admitting that you disagree with them, but you insist that your disagreement with them is that they don't say what they evidently say that they are saying.

Never mind: I gave that reference not to you but to Jeroen for consideration. I'll abstain from further comments until he reacts.

 

[PAllen]

Of course that can't be what he means, but you insist that it is what he means. Thus in the end you cannot avoid admitting that you disagree with them, but you insist that your disagreement with them is that they don't say what they evidently say that they are saying.

.

No, I disagree with what you say they are saying. I have no problem with what they are saying about the classical case, as I understand it, in full context. I also think there is no disagreement on what their new quantum claim is. (There is, of course, disagreement on whether the new claim is true, and that will not be settled until quantum gravity is settled).

[Edit: appear is the author's own words. I am taking them at what they say, literally. They then give more meaning to this classical statement when quantum affects are considered. To me, it is totally obvious that you are distorting a paper aimed proposing a solution to the quantum BH information paradox via a quantum analysis of collapse that removes the problem => into a paper claiming new classical results. ]

 

[harrylin]

No, I disagree with what you say they are saying.

While I don't comment on the paper anymore, I can't resist commenting on the following comment by you, which is regretfully just one example of too many of such:

[..] To me, it is totally obvious that you are distorting a paper aimed proposing a solution to the quantum BH information paradox via a quantum analysis of collapse that removes the problem => into a paper claiming new classical results. ]

My understanding of that paper is that it does not propose new classical results but a controversial interpretation of classical results that matches their quantum results. And you misunderstand with who you were disagreeing in your latest comments. As a reminder:

what is controversial about the new finding is that "from an external viewer's point it takes an infinite amount of time to form an event horizon and that the clock for the objects falling into the black hole appears to slow down to zero," said Krauss, director of Case's Center for Education and Research in Cosmology.

- News center of Case Western Reserve University
http://blog.case.edu/case-news/2007/06/20/blackholes

The controversy is over the new claim: that the competition between evaporation and collapse is won by evaporation.

- comment of PAllen
https://www.physicsforums.com/showpost.php?p=4164539&postcount=18

 

[PAllen]

My understanding of that paper is that it does not propose new classical results but a controversial interpretation of classical results that matches their quantum results. And you misrepresent with who you were disagreeing there.

Actually, with this I can agree - the key point being that the controversial interpretation of classical GR (effectively, that only exterior SC coordinates are physically meaningful), is viable only as a consequence of the quantum modeling (which is covered as prelude to the statement you refer). In short, everything proposed in the paper stands or falls on their quantum simulation.

 

[harrylin]

[..] the [..] interpretation [..] that only exterior SC coordinates are physically meaningful [..] is viable only as a consequence of the quantum modeling [..]

That doesn't make any logical sense to me; but that discussion is for another thread. Maybe we can fit it in your simultaneity topic.

[ADDENDUM: it suddenly does make sense to me: you seem to think that there is a paradox without evaporation. I don't think so; to the contrary it solves a paradox. We'll discuss that in your simultaneity thread. ]

 

[PAllen]

That doesn't make any logical sense to me; but that discussion is for another thread. Maybe we can fit it in your simultaneity topic.

[ADDENDUM: it suddenly does make sense to me: you seem to think that there is a paradox without evaporation. I don't think so; to the contrary it solves a paradox. We'll discuss that in your simultaneity thread. ]

Belabored as discussion of this paper is, I do want to provide one bit of context for some wording in the paper.

Well known, and non-controversial, prior to Krauss et.al. is that classically a collapse is never observed to reach an event horizon from outside; and the arrival of the surface at the event horizon takes infinite Schwarzschild time. At the same time, for a long time, it has also been understood that in other coordinates, the collapse takes finite coordinate time; and clock falling with the matter crosses the horizon in finite time (as well as reaching the singularity in finite time). Krauss et.al mention this only obliquely via reference to known defects of Schwarzschild coordinates. Also, prior to this paper, a number of quantum results (see Krauss et.al.'s footnote 3, early in the paper) suggested that quantum corrections would make the horizon form in finite time as directly observed by an outside observer; further, it would form in finite Schwarzschild coordinate time. This obviously makes quantum analysis of the horizon and interior an acute issue, as well as reinforcing the quantum information paradox.

Krauss et. al. are disputing this, and that is the meaning of:"We find that even in this case [quantum treatment] the black
hole takes an infinite time to form, contrary to some speculations
in the literature [3]."

Then, if Krauss et.al. are right (including the fact that all matter of the collapsed shell has evaporated before the event horizon has formed, which is the key quantum result), it makes sense to declare that even classically there is no point in asking about the future of clocks seen to stop externally - because they believe such clocks will evaporate in finite time without ever being inside an event horizon. It is only based on this that it makes sense to 'chop' the classical picture before formation of the event horizon. And this is exactly how I read the press release as well as the paper.

Padmanabhan and others, of course, dispute this finding, and the debate will continue.