FLUX-AREA OPERATOR AND BLACK HOLE ENTROPY

摘要

The computation of black hole entropy in loop quantum gravity is based on a nonperturbative 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 loop quantum gravity. This flux-area operator has a discrete spectrum with equidistant eigenvalues that coincide with the prequantized areas of the U(1) 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 explore the consequences of this substitution in the Ashtekar-Baez-Corichi-Krasnov definition of the black hole entropy. We discuss 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 for the quantum geometry.