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A fascinating solution of the black-hole information problems?

  1. Mar 30, 2012 #1


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    We study a self-consistent solution of the semi-classical Einstein equation including the back reaction from the Hawking radiation. Our geometry is constructed by connecting flat space and the outgoing Vaidya metric at the locus of the shock wave. In order to prove that this is the self-consistent solution, we first show that the Weyl anomaly is canceled if we take the effects of the fluctuations of the metric into account. We further demonstrate that the Hawking radiation occurs even if the geometry has no horizon. Then, the energy-momentum tensor is found to be consistent with the semi-classical Einstein equation. Since our geometry has neither horizon nor singularity, all matters inside the black hole finally come back to infinity. Therefore, no information is lost by the black hole evaporation. Furthermore, we take into account the gray-body factor. We construct a stationary solution for a black hole in the heat bath and estimate the entropy. The entropy-area law is reproduced by the volume integration of the entropy density over the inside of the horizon, and the black hole can be treated as an ordinary thermodynamic object.

    If it does not contain serious errors or unjustified approximations (which in a first reading I was not able to identify), it sounds really fascinating. What do you think?
  2. jcsd
  3. Mar 30, 2012 #2
    all matters inside the black hole finally come back FROM infinity?...Fixed? :/
  4. Mar 30, 2012 #3


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    It would be interesting to compare this to fuzzball GR solutions which also avoid horizon and singularity (you only get something that looks like a horizon macroscopically).

    [edit: I guess the biggest difference is that, at least in the fuzzball paper I checked, extra dimensions are required. This paper achieves its result without extra dimensions. This paper is really 'hot off the press'. I am, indeed, fascinated. Will try to read it more.]
    Last edited: Mar 30, 2012
  5. Mar 31, 2012 #4
    In how far is there actually anything left to explain? I mean, in Wilczek and Parik's tunneling formalism, it's been known for a while that (non-classical) correlations exist between the black hole and the outgoing radiation, accounting for the unitarity of black hole evaporation, right? (Here's a paper brought up by quick googling, though I'm not sure it's the one I had in mind.) Assuming this holds, is there anything beyond that in need of explanation?
  6. Mar 31, 2012 #5
    Boffo introductory explanation and claims: WOW!!

    cool diagrams!!

    I find the following confusing...not impossible, just confusing....but then I am frequently confused!! I got 'stuck' right here:


    ok let's assume objects 'stick' to the horizon....why would the horizon vanish faster than the stuck information? Does the emitted radiation/information depart before the collapse
    Is that the description used so far with black hole horizons...or is this an 'exotic' extrapolation? Is it even important? Is the observer 'at infinity' linked to the ideal Schwarszchild metric currently used in explanations???

    Reflection by Gravitationa potential..//pg 12

    This doesn't sound like radiation getting out faster than the horizon collapse:
    "The radiation leaves the shock wave surface and goes outward for a while. Then a part of it tunnels through the potential with the probability P. The other part is scattered by the gravitational potential with the probability 1−P and comes back. This is nothing but the effect of the gray-body factor.2 The black hole is not a perfect black body, and a part of the Hawking radiation comes back to the hole again...."

    Conclusions ......
    Paradigm changing if accurate: [Bekenstein-Hawking entropy
    "..It is rather striking that the volume integral over the
    inside leads to the area law, which may indicate that microstates that contribute to the entropy live not on the surface but inside..." Leonard Susskind may go NUTS!!!

    "..This leads to the very high local temperature. [I don't get that. local not large scale??] .....
    However, these values are finite, and a similar problem has been known as the trans-Planckian problem since the Hawking radiation was discovered [31, 32]. In addition, the behavior at r = 0 and the final stage of the evaporation has not been studied in our analysis. These problems might be resolved only by an ultraviolet complete theory such as string theory.

    Where is Susskind and his strings?
    Last edited: Mar 31, 2012
  7. Mar 31, 2012 #6
    And in Susskind's string studies.....

    This is the first instance I've seen of particle pair production
    without an event horizon...I posted a related question with horizons just today:

    Does Born rigidity describe particle creation?

    Last edited: Mar 31, 2012
  8. Apr 2, 2012 #7


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    I think the main problem with tunneling approaches to black-hole evaporation is the fact that such approaches assume that escaping from a black hole through a horizon is just an example of escaping through a classical barrier. But it is not. In ordinary quantum mechanics, a classical particle with too-small energy cannot transit the potential barrier, but the wave with same energy satisfying the wave equation can. That's why quantum particle can escape from a classical barrier. But the horizon is different, because even the relativistic wave satisfying the wave equation in a black-hole background cannot transit through the horizon. (If it could, then the group velocity of the wave would be faster than light, which is not the case.)

    The calculation of tunneling by Parikh, Wilczek and others is not based on actual calculation of the wave function traveling through the horizon (because it would not lead to a desired result), but is based on the WKB approximation. Hence, the WKB approximation seems highly unjustified in that case.
  9. Apr 2, 2012 #8


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    I think the biggest difference is that the present approach is based on SEMICLASSICAL gravity, so does not depend on details of quantum gravity, whatever the final theory of which eventually might turn out to be (strings or something else). This includes extra dimensions, branes, quantum hairs, weak/strong duality, AdS/CFT, and other exotic stuff that string theory brings, none of which playing any role in the present approach.
  10. Apr 2, 2012 #9


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    Actually, the fuzzball treatment can start with classical solution of GR with extra dimensions. You arrive at purely classical solutions with no horizon or singularity - but they need the extra dimensions.

    [Edit: some doubt about the above; I may be misreading some of these results. I do note the following:

    "A primitive form of the complaint is the following: “Your fuzzball solutions are classical
    metrics. A state of a black hole must be a quantum state. So how can fuzzballs have anything
    to do with microstates of black holes?”."

    from section 10 of: http://arxiv.org/abs/arXiv:1108.0302

    Last edited: Apr 2, 2012
  11. Apr 2, 2012 #10


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    Are these solutions static? If yes, what a static solution without horizon has to do with black holes?
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