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A Entropy bounds

  1. Aug 11, 2018 #1

    martinbn

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    There is something that is unclear to me, and because entropy bounds and their violations were discussed in the other thread, I thought it is a good opportunity to learn something. The problem is essentially a matter of impression. The statements go roughly in the following way: for a system with entropy ##S## and energy ##E##, which is contain in space of radius ##R## a certain inequality involving the above must hold. The problem for me is that the ##E## and the ##R## are never defined (well, I haven't seen it, it might very well be explained somewhere). And in a general relativistic setting they are meaningless.

    So the question is how does one make the statements precise?
     
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  3. Aug 11, 2018 #2

    PeterDonis

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    The precise definition of the Bekenstein bound is that the entropy of an object with externally measured mass ##M## and enclosed within a surface with surface area ##A## must be less than or equal to the entropy of a black hole with mass ##M## and horizon area ##A##. The latter has a precise formula first derived by Hawking, which amounts to the entropy being the log of the horizon area divided by the Planck area.
     
  4. Aug 12, 2018 #3

    martinbn

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    The surface area is better than the vague ##R##, but it still depends on the space-like slice. And how is the mass defined?
     
  5. Aug 12, 2018 #4

    PeterDonis

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    Technically, yes, but for an asymptotically flat (i.e., isolated) system, one can define what amounts to a center of mass frame and use that to define the spacelike slices. Until we get a proper theory of quantum gravity, that's probably the best we're going to be able to do, since without one we simply don't know the precise microscopic degrees of freedom of a system including the spacetime geometry.

    The ADM mass or the Bondi mass would be the simplest definitions, since they apply to any asymptotically flat system. I would lean towards the latter since it takes into account radiation emitted out to infinity.
     
  6. Aug 22, 2018 #5

    Demystifier

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    I think this could be the answer:
    https://arxiv.org/abs/hep-th/9905177
     
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