Covariant entropy bound beyond general relativity

Abstract

We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald entropy or its extension instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in four-dimensional GR to D-dimensional GR, f(R) gravity, and canonical scalar-tensor theory. We then consider Einstein-Gauss-Bonnet (EGB) gravity as a more nontrivial example and, under a set of reasonable assumptions, prove the bound in the GR branch of spherically symmetric configurations. As a corollary, it is shown that under the null and dominant energy conditions, the generalized second law holds in the GR branch of spherically symmetric configurations of EGB gravity at the fully nonlinear level.