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Life below the Schwarzschild radius

  1. Nov 11, 2012 #1
    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? :)
  2. jcsd
  3. Nov 11, 2012 #2


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    Hi JeroenDeDauw, welcome to PF!

    What is a region of maximum entropy? Does entropy even have a maximum?
  4. Nov 11, 2012 #3


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    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:

  5. Nov 11, 2012 #4


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    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.)
    Last edited: Nov 11, 2012
  6. Nov 12, 2012 #5


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    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.
  7. Nov 16, 2012 #6
    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.
  8. Nov 17, 2012 #7
    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:
  9. Nov 17, 2012 #8


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    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:


    (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).
  10. Nov 17, 2012 #9
    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. :grumpy:

    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
  11. Nov 17, 2012 #10


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    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.
  12. Nov 17, 2012 #11


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    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.
  13. Nov 18, 2012 #12
    Then this topic belongs in the General Physics forum. Can it be moved?
  14. Nov 18, 2012 #13
    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)
  15. Nov 18, 2012 #14


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    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.
  16. Nov 18, 2012 #15


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    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.
  17. Nov 18, 2012 #16
    (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."
    Or, better, from their own press department "Black holes don't exist, Case physicists report":
    I suggest to ask Susan Griffith if you still don't believe it. :wink:

    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.
    Last edited: Nov 18, 2012
  18. Nov 18, 2012 #17
    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 :smile:

    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.
    Last edited: Nov 18, 2012
  19. Nov 18, 2012 #18


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    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.
    It is wide open in with quantum effects considered. It is not open classically.
  20. Nov 18, 2012 #19
    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. :uhh:

    Never mind: I gave that reference not to you but to Jeroen for consideration. I'll abstain from further comments until he reacts.
  21. Nov 18, 2012 #20


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    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. ]
    Last edited: Nov 18, 2012
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