MG12 - Talk detail
 

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 Participant 

Institution

Session

Talk

Abstract

Black hole entropy in loop quantum gravity

I will discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the number-theoretical methods recently developed. In particular, I will give the complete characterization of the relevant sector of the spectrum of the area operator -including degeneracies- and a procedure to find the number of solutions to the projection constraint for spherical black holes. I will also introduce a set of generating functions that solve all the different combinatorial problems that crop up in the study of black hole entropy in loop quantum gravity. Specifically, I will give generating functions for: The different sources of degeneracy related to the spectrum of the area operator, the solutions to the projection constraint, and the black hole degeneracy spectrum. Finally, I will derive exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area and I will discuss the delicate issue of the asymptotics of black hole entropy.

Flux-area operator and black hole entropy in loop quantum gravity

The ABCK approach to the computation of black hole entropy in loop quantum gravity is based on a non-perturbative quantization derived from a Hamiltonian formulation of general relativity on a 3-manifold with a spherical inner boundary. We show that the extra, non-dynamical, structure provided by this inner boundary allows us to define a natural area operator different from the standard one used in LQG. This flux-area operator has a discrete spectrum with equidistant eigenvalues coinciding with the prequantized areas of the Chern-Simons theory used to model the horizon quantum degrees of freedom. The matching between the horizon Chern-Simons theory and the bulk quantum geometry is arguably more natural with the new choice of area operator. We discuss the consequences of this substitution in the ABCK definition of the black hole entropy and obtain closed, and rather simple, expressions for it. Finally we look at the compatibility of our results with the Bekenstein-Hawking area law and show how the link with quasinormal modes can be restored while still using SU(2) as the internal symmetry group.

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