Generating functions for black hole entropy in Loop Quantum Gravity

Details Generating functions for black hole entropy in Loop Quantum Gravity Generating functions for black hole entropy in Loop Quantum Gravity

2008-04-30

arxiv.org/abs/0804.4784v1

Phys.Rev.D77:121502,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

nine pages

Scientific paper

10.1103/PhysRevD.77.121502

We introduce, in a systematic way, 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 we 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. Our methods are capable of handling the different countings proposed and discussed in the literature. The generating functions presented here provide the appropriate starting point to extend the results already obtained for microscopic black holes to the macroscopic regime --in particular those concerning the area law and the appearance of an effectively equidistant area spectrum.

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