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arXiv · hep-th/9512184

Black Hole Entropy: Off-Shell vs On-Shell

V. P. Frolov·D. V. Fursaev·A. I. Zelnikov
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Abstract

Different methods of calculation of quantum corrections to the thermodynamical characteristics of a black hole are discussed and compared. The relation between on-shell and off-shell approaches is established. The off-shell methods are used to explicitly demonstrate that the thermodynamical entropy $S^{TD}$ of a black hole, defined by the first thermodynamical law, differs from the statistical-mechanical entropy $S^{SM}$, determined as $S^{SM}=-\mbox{Tr}(\hatρ^H\ln\hatρ^H)$ for the density matrix $\hatρ^H$ of a black hole. It is shown that the observable thermodynamical black hole entropy can be presented in the form $S^{TD}=π{\bar r}_+^2+S^{SM}-S^{SM}_{Rindler}$. Here ${\bar r}_+$ is the radius of the horizon shifted because of the quantum backreaction effect, and $S^{SM}_{Rindler}$ is the statistical-mechanical entropy calculated in the Rindler space.

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V. P. Frolov, D. V. Fursaev, A. I. Zelnikov. 1995-12-28. Black Hole Entropy: Off-Shell vs On-Shell. https://doi.org/10.1103/physrevd.54.2711

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