Black Hole Entropy: Off-Shell vs On-Shell

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 ${\hat{\rho }}^H$ of a black hole. It is shown that the observable thermodynamical black hole entropy can be presented in the form $S^{TD}=\pi {\bar{r}}_{+}^2+S^{SM}-S_{Rindler}^{SM}$. Here ${\bar{r}}_{+}$ is the radius of the horizon shifted because of the quantum backreaction effect, and $S_{Rindler}^{SM}$ is the statistical-mechanical entropy calculated in the Rindler space.

47 pages, latex, 7 postscript figures have been included since the first submission of the article

References in corpus (3)

• Black Hole Entropy in the O(N) Model
• Two-dimensional Quantum-Corrected Eternal Black Hole
• Finite Temperature Effects for Massive Fields in D-dimensional Rindler-like Spaces

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