Thermodynamics of a black hole based on a generalized uncertainty principle

Details Thermodynamics of a black hole based on a generalized uncertainty principle Thermodynamics of a black hole based on a generalized uncertainty principle

2007-11-06

arxiv.org/abs/0711.0786v2

JHEP0801:035,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 4 figures; v2. to appear in JHEP

Scientific paper

10.1088/1126-6708/2008/01/035

We study thermodynamic quantities and the stability of a black hole in a cavity using the Euclidean action formalism by Gibbons and Hawking based on the generalized uncertainty relation which is extended in a symmetric way with respect to the space and momentum without loss of generality. Two parameters in the uncertainty relation affect the thermodynamical quantities such as energy, entropy, and the heat capacity. In particular, it can be shown that the small black hole is unstable and it may decay either into a minimal black hole or a large black hole. We discuss a constraint for a large black hole comparable to the size of the cavity in connection with the critical mass.

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