A Second Law for Higher Curvature Gravity

TL;DR

This paper demonstrates that the Second Law of black hole thermodynamics holds in higher curvature gravity theories under linearized perturbations, connecting it with holographic entanglement entropy and addressing ambiguities in existing methods.

Contribution

It shows the validity of the Second Law in complex higher curvature gravity theories for linearized perturbations and clarifies ambiguities in Wald's Noether charge approach.

Findings

The Second Law holds for higher curvature gravity under linearized perturbations.

The increasing quantity matches holographic entanglement entropy as per Dong.

Ambiguities in Wald's Noether charge method are resolved.

Abstract

The Second Law of black hole thermodynamics is shown to hold for arbitrarily complicated theories of higher curvature gravity, so long as we allow only linearized perturbations to stationary black holes. Some ambiguities in Wald's Noether charge method are resolved. The increasing quantity turns out to be the same as the holographic entanglement entropy calculated by Dong. It is suggested that only the linearization of the higher-curvature Second Law is important, when consistently truncating a UV-complete quantum gravity theory.