Toward explaining black hole entropy quantization in loop quantum gravity

Details Toward explaining black hole entropy quantization in loop quantum gravity Toward explaining black hole entropy quantization in loop quantum gravity

2007-09-15

arxiv.org/abs/0709.2433v3

Phys.Rev.D76:104050,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 5 figures. v3: final version (essentially as it appeared in PRD)

Scientific paper

10.1103/PhysRevD.76.104050

In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this step-like behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking.

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