Black Hole Entropy

TL;DR

This paper compares different definitions of black hole entropy, highlighting differences between the Bekenstein-Hawking entropy and statistical-mechanical entropy, and explains the universality of the former.

Contribution

It clarifies the distinction between thermodynamic and statistical definitions of black hole entropy and explains why Bekenstein-Hawking entropy is universal.

Findings

Bekenstein-Hawking entropy differs from statistical-mechanical entropy.

Bekenstein-Hawking entropy is universal, independent of field properties.

The paper provides an explanation for the universality of Bekenstein-Hawking entropy.

Abstract

In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy $S^{BH}$ (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy $S^{SM}=-\mbox{Tr}(\hat{\rho}\ln \hat{\rho})$ (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (i.e. its independence of the number and properties of the fields which might contribute to $S^{SM}$) is given.