Generating functions for black hole entropy in Loop Quantum Gravity

Abstract

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.

nine pages

References in corpus (9)

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Cited by in corpus (19)

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• Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
• Flux-area operator and black hole entropy
• Static isolated horizons: SU(2) invariant phase space, quantization, and black hole entropy
• On the computation of black hole entropy in loop quantum gravity
• Probing Loop Quantum Gravity with Evaporating Black Holes
• Statistical description of the black hole degeneracy spectrum
• A topological limit of gravity admitting an SU(2) connection formulation
• Entropy of black holes with arbitrary shapes in loop quantum gravity
• Entropy of Quantum Black Holes
• The thermodynamic limit and black hole entropy in the area ensemble
• Computing Black Hole entropy in Loop Quantum Gravity from a Conformal Field Theory perspective
• Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity
• The thermodynamics of isolated horizons in loop quantum gravity
• Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations
• Entropy in Spin Foam Models: The Statistical Calculation