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Abstract: In a remarkable numerical analysis of the spectrum of states for aspherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Poloand Fernandez-Borja found that the entropy of the black hole horizon increasesin what resembles discrete steps as a function of area. In the present articlewe reformulate the combinatorial problem of counting horizon states in terms ofpaths through a certain space. This formulation sheds some light on the originsof this step-like behavior of the entropy. In particular, using a few extraassumptions we arrive at a formula that reproduces the observed step-length toa few tenths of a percent accuracy. However, in our reformulation theperiodicity ultimately arises as a property of some complicated process, theproperties of which, in turn, depend on the properties of the area spectrum inloop quantum gravity in a rather opaque way. Thus, in some sense, a deepexplanation of the observed periodicity is still lacking.



Autor: Hanno Sahlmann

Fuente: https://arxiv.org/







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