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There is a rather intersting paper from Sorkin:
http://arxiv.org/abs/hep-th/0504037
Ten Theses on Black Hole EntropyAuthors: Rafael D. Sorkin (Perimeter Institute and Syracuse University)
(Submitted on 5 Apr 2005 (v1), last revised 19 Oct 2011 (this version, v2))
Abstract: I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon "degrees of freedom"; is finite because the deep structure of spacetime is discrete; is "objective" thanks to the distinguished coarse graining provided by the horizon; and obeys the second law of thermodynamics precisely because the effective dynamics of the exterior region is not unitary.
I just want to stress the following [Sorkin]
Thesis 1: The most natural explanation of the area law is that S resides on the horizon.
Thesis 4: The idea that the degrees of freedom are inside the black hole is wrong.
Thesis 9: To understand the generalized second law requires a spacetime approach, not a canonical one.
His reasoning regarding thesis 9 is striking and I would like to interpret as follows: 'locating' the degrees of freedom on a surface would require somehow to 'locate' this surface in spacetime; but for lightlike surfaces it is hopeless to 'locate' or 'embed' the surface in a spacelike slice or to reconstruct a non-spacelike horizon in a semiclassical approach on a spacelike slice which is used in canonical approach.
http://arxiv.org/abs/hep-th/0504037
Ten Theses on Black Hole EntropyAuthors: Rafael D. Sorkin (Perimeter Institute and Syracuse University)
(Submitted on 5 Apr 2005 (v1), last revised 19 Oct 2011 (this version, v2))
Abstract: I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon "degrees of freedom"; is finite because the deep structure of spacetime is discrete; is "objective" thanks to the distinguished coarse graining provided by the horizon; and obeys the second law of thermodynamics precisely because the effective dynamics of the exterior region is not unitary.
I just want to stress the following [Sorkin]
Thesis 1: The most natural explanation of the area law is that S resides on the horizon.
Thesis 4: The idea that the degrees of freedom are inside the black hole is wrong.
Thesis 9: To understand the generalized second law requires a spacetime approach, not a canonical one.
His reasoning regarding thesis 9 is striking and I would like to interpret as follows: 'locating' the degrees of freedom on a surface would require somehow to 'locate' this surface in spacetime; but for lightlike surfaces it is hopeless to 'locate' or 'embed' the surface in a spacelike slice or to reconstruct a non-spacelike horizon in a semiclassical approach on a spacelike slice which is used in canonical approach.
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