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arXiv · 0709.2433

Toward explaining black hole entropy quantization in loop quantum gravity

Hanno Sahlmann
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Abstract

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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Hanno Sahlmann. 2007-11-29. Toward explaining black hole entropy quantization in loop quantum gravity. https://doi.org/10.1103/physrevd.76.104050

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