Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity

TL;DR

This paper proves that in Einstein-Gauss-Bonnet gravity, the entropy of a black hole increases during small perturbations, extending the physical process first law to higher curvature theories.

Contribution

It establishes the physical process first law for black holes in Einstein-Gauss-Bonnet gravity, showing entropy increase under perturbations satisfying null energy conditions.

Findings

Wald entropy increases during perturbations

First law holds in Einstein-Gauss-Bonnet gravity

Black hole stability under small perturbations

Abstract

We establish the physical process version of first law by studying small perturbations of a stationary black hole with regular bifurcation surface in Einstein-Gauss-Bonnet (EGB) gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies null energy condition.