Schwarzschild black hole as a grand canonical ensemble

Details Schwarzschild black hole as a grand canonical ensemble Schwarzschild black hole as a grand canonical ensemble

1999-07-21

arxiv.org/abs/gr-qc/9907066v2

Phys.Rev.D61:021501,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTex, 10 pages, Accepted for publication in Physical Review D

Scientific paper

10.1103/PhysRevD.61.021501

For long black holes have been considered as endowed with a definite temperature. Yet when the Schwarzschild black hole is treated as a canonical ensemble three problems arise: incompatibility with the Hawking radiation, divergence of the partition function, and a formally negative mean-square fluctuation of the energy. We solve all three problems by considering the Schwarzschild black hole as a grand canonical ensemble, with the Hamiltonian (the ADM mass) and the horizon surface area, separately, as observable parameters. The horizon area simulates the number of particles in statistical mechanics since its spectrum is assumed to be discrete and equally spaced. We obtain a logarithmic correction to the Bekenstein-Hawking entropy and a Gaussian type distribution for the energy levels.

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