Black Hole Entropy: Thermodynamics, Statistical-Mechanics and Subtraction Procedure

Abstract

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 $-Tr\hat{\rho }\ln \hat{\rho }$ 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.

11 pages, latex file

References in corpus (3)

• Black Hole Entropy and Entropy of Entanglement
• Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant
• Thermodynamics of Quantum Fields in Black Hole Backgrounds

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