Black hole entropy: thermodynamics, statistical-mechanics and subtraction procedure

The thermodynamical one-loop entropy S TD of a two-dimensional black hole in thermal equilibrium with the massless quantum gas is calculated. It is shown that S TD includes the Bekenstein-Hawking entropy, evaluated for the quantum corrected geometry, and the finite difference of statistical mechanic...

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Bibliographic Details
Published in:Physics letters. B 1996-08, Vol.382 (3), p.220-226
Main Authors: Frolov, V.P., Fursaev, D.V., Zelnikov, A.I.
Format: Article
Language:English
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Summary:The thermodynamical one-loop entropy S TD of a two-dimensional black hole in thermal equilibrium with the massless quantum gas is calculated. It is shown that S TD includes the Bekenstein-Hawking entropy, evaluated for the quantum corrected geometry, and the finite difference of statistical mechanical entropies — Tr ϱ ln ϱ for the gas on the black hole and Rindler spaces. This result demonstrates in an explicit form that the relation between thermodynamical and statistical-mechanical entropies of a black hole is non-trivial and requires special subtraction procedure.
ISSN:0370-2693
1873-2445
DOI:10.1016/0370-2693(96)00661-2