Black Hole Entropy and Boundary Conditions

TL;DR

This paper explores how different boundary conditions and Gibbons-Hawking-York terms influence black hole entropy, finding that entropy remains consistent across various boundary conditions in both GR and f(R)-gravity.

Contribution

It demonstrates that black hole entropy is invariant under different boundary conditions and associated GHY terms in both general relativity and f(R)-gravity.

Findings

Black hole entropy is unaffected by boundary condition choices.

Entropy matches Wald formula regardless of boundary conditions.

Results hold for Schwarzschild solutions in GR and f(R)-gravity.

Abstract

It is well-known that in order to make the action well defined, one may employ different kinds of boundary conditions (BCs) accompanied by the appropriate Gibbons-Hawking-York (GHY) terms. In this paper we investigate the role of the selected BC and the corresponding GHY terms on the black hole (BH) entropy. Our result shows, regardless of the kind of BC, the BH entropy in all cases is the same as one obtained under Dirichlet BC from Wald formula or semi-classical approximation method. We considered the Schwarzschild solution for $f(R)$-gravity and general relativity (GR) in standard dimensions as special models.