Covariant entropy bound beyond general relativity

TL;DR

This paper extends the covariant entropy bound to gravitational theories beyond general relativity by using Wald-Jacobson-Myers entropy, proving it in various theories including Einstein-Gauss-Bonnet gravity, and confirms the generalized second law under certain conditions.

Contribution

It introduces a covariant entropy bound applicable to non-GR theories using Wald-Jacobson-Myers entropy and proves it in multiple extended gravity models.

Findings

Proved the entropy bound in D-dimensional GR, f(R) gravity, and scalar-tensor theories.

Established the bound in Einstein-Gauss-Bonnet gravity under specific assumptions.

Showed the generalized second law holds in EGB gravity's spherically symmetric configurations.

Abstract

We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald-Jacobson-Myers entropy instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in 4-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 non-trivial 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.