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The horizon

  1. Apr 28, 2004 #1
    This is a thread attempting to comprehend the physics behind the theory in the description of Black holes in LQG.
    There has been very much debate about the minimum value that a puncture can have in the horizon of a BH. The fact is, if a puncture disappears from the horizon, then the horizon reduces its area. It suggests that in LQG the horizon is something real, has physical existence. Do you get the point? In GR, the horizon is something theoretical, there's not a real spherical sheet surrounding the BH. But here the things seem different. Then my question is : what's this material that composes the horizon in LQG? What's the horizon made of?
    another question is: Is in LQG a black hole still a singularity? If not, there's some formula that relates its mass with its volume?
     
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  3. Apr 28, 2004 #2

    marcus

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    To me it seems as if the horizon is equally real (and unreal) in GR and LQG.
    The way I understand the horizon, it is something determined by the gravitational field. If I think of the field as a real thing (though not made of any material) then the horizon that it defines is equally real (but also not made of any material)

    the business about punctures has more to do with how a pure quantum state is represented in LQG (as a spin network---or equivalence class of spin networks) and how the area of a surface is calculated using a particular quantum state. I am certainly not clear on every detail of this but I dont think the idea is that the horizon surface is any more real or less real than it is in classical GR.

    I hope very much that others will respond (stingray, nonunitary, arivero, hellfire, haelfix are possibilities) who understand the question since I feel I am missing the point
     
    Last edited: Apr 28, 2004
  4. Apr 28, 2004 #3

    marcus

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    this is an exciting unanswered question AFAIK

    no one can say if LQG will succeed or fail as a theory of gravity but
    if it succeeds it should describe what is at the Schwarzschild BH singularity.

    You know that starting around 2001 Bojowald and others have made some progress understanding the BigBang singularity. How, when the cosmological model is quantized, there is no singularity but a kind of planck scale turmoil during which contraction is converted into expansion.

    So I have been waiting for some quantum gravitist to (in a similar way) analyze the Black Hole singularity---so that in a quantum model it too can perhaps go away or stop being a singularity.

    I hope for quantum gravitists to suggest an idea of what happens to the matter, when it is crushed.

    But so far I havent seen any LQG paper about this.

    There are interesting papers (like the J. Graber 1999 papers) about
    what could be happening inside BH, but I cant tell how these papers are received or how they fit in to the overall picture.

    Some people are giving answers, maybe, but so far there is no specifically LQG answer to this puzzle. That I know of at least. Does anyone know of LQG investigation of the BH singularity?
     
  5. Apr 28, 2004 #4
    The determination of area in quantum geometry is the same spirit as for classical gr. In classical GR, there is a bare 4-dimensional manifold with some topology. You solve Eintein's field equations to determine the metric on this bare manifold. The metric gives you notions of geometry, including areas of space.

    Similarly, in quantum geometry, there is a bare manifold (but now 3 dimensional). A spin network is embedded in this manifold. The geometry is determined by the eignevalues of the geometric operators, like area. The bare manifold here has notions of continuity (that's part of the definition of a manifold) but this should not be mistaken as being the space part of spacetime itself. The manifold is auxilliary in the sense that the embedding of the spin network gives meaning to notions of space (that is, it gives rise to the geometry of space, which is the thing that can be probed).

    The "stuff" that is present in any case is spacetime, a dynamical entity, be it smooth or "atomized". A black hole is an object purely described by spacetime geometry. It is a sort of whirlpool where the behavior of the water outside and inside the edge of the whirlpool is very different. In this case, it is the spacetime geometry that is quite different on either side of the horizon.
    Other than entropy of horizon calculations, it is difficult to do anything with black holes since they are an entity described by space*time* geometry, and time is a problem in a real formulation of the quantum geometry program (spin networks are *spatial* states). Of course, since space is atomized in this construction, singularities are not expected in any case.

    Regarding your last question: mass is an effective notion for a black hole...it is in terms of a global energy determined by the curvature tensor for the particular geometry. The problem remains to understand "curvature" and "energy content" in terms of spin networks. Trying to get Minkowski spacetime out of the whole deal is a good program to understand the connection between classical GR notions and the quantum ones, and that is part of what is going on at the CGPG.

    By the way, spin foams are an alternative way to tackle the whole problem: instead of handling space and time separately, it handles it all together (this is the so-called covariant quantization as opposed to the canonical quantization which the quantum geometry program is). Again, there are thorny issues here as well.
     
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