Black Hole Entropy: Off-Shell vs On-Shell

Frolov, V. P.; Fursaev, D. V.; Zelnikov, A. I.

Black Hole Entropy: Off-Shell vs On-Shell

Authors

Frolov, V. P.

Fursaev, D. V.

Zelnikov, A. I.

Description

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