Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-04-06
Phys.Rev.D52:3529-3542,1995
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, latex, no figures. References added, minor error corrected
Scientific paper
10.1103/PhysRevD.52.3529
We discuss the relation between the micro-canonical and the canonical ensemble for black holes, and highlight some problems associated with extreme black holes already at the classical level. Then we discuss the contribution of quantum fields and demonstrate that the partition functions for scalar and Dirac (Majorana) fields in static space-time backgrounds, can be expressed as functional integrals in the corresponding optical space, and point out that the difference between this and the functional integrals in the original metric is a Liouville-type action. The optical method gives both the correction to the black hole entropy and the bulk contribution to the entropy due to the radiation, while (if the Liouville term is ignored) the conical singularity method just gives the divergent contribution to the black hole entropy. A simple derivation of a general formula for the free energy in the high-temperature approximation is given and applied to various cases. We conclude with a discussion of the second law.
de Alwis Senarath P.
Ohta Nobuyoshi
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