Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-12-22
Phys.Rev.D54:2711-2731,1996
Physics
High Energy Physics
High Energy Physics - Theory
47 pages, latex, 7 postscript figures have been included since the first submission of the article
Scientific paper
10.1103/PhysRevD.54.2711
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 $S^{SM}=-\mbox{Tr}(\hat{\rho}^H\ln\hat{\rho}^H)$ 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 $S^{TD}=\pi {\bar r}_+^2+S^{SM}-S^{SM}_{Rindler}$. 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.
Frolov Valeri P.
Fursaev Dmitri V.
Zelnikov A. I.
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