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Is gravitational entropy quantized ? · Around

2008

Is gravitational entropy quantized ?

Kothawala, Dawood, Padmanabhan, T., Sarkar, Sudipta

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In Einstein's gravity, the entropy of horizons is proportional to their area.

Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equally spaced spectrum for large quantum numbers.
But in more general theories (like, for e.g, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is \emph{not} proportional to area and the question arises as to which of the two (if at all) will have this property.
We give a general argument that in all Lanczos-Lovelock theories of gravity, it is the \emph{entropy} that has equally spaced spectrum.

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C. Lanczos, Z.Phys. 73
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T. Padmanabhan, Apoorva Patel [gr-qc/0309053], T. Padmanabhan, Phys. Reports, 406, 49, (2005) [gr-qc/0311036]. The arguments were given for the case of Einstein’s theory in these references but they continue to be valid for any gravitational action
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This result only depends on spherical symmetry and the first law of black hole thermodynamics, and can be easily extended to black holes in Gauss-Bonnet gravity, leading to the same result for minimum increase of entropy

Then

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T. Padmanabhan, Gen.Rel.Grav
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Maggiore, Michele, Phys. Rev. Lett. 100, 141301, (2008)
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Elias C. Vagenas [arXiv:0804.3264v2]; A.J.M. Medved [arXiv:0804.4346v2]

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