The second law of black hole mechanics in effective field theory

TL;DR

This paper extends the understanding of black hole entropy and the second law in theories with higher derivative gravity, using effective field theory to ensure the law holds beyond linear perturbations.

Contribution

It generalizes Wall's method to quadratic order in perturbations, addressing gauge invariance and relation to Iyer-Wald entropy in higher derivative theories.

Findings

Second law holds to quadratic order with effective field theory treatment.

Extended Wall's method to address gauge invariance issues.

Clarified relation between Wall's entropy and Iyer-Wald entropy.

Abstract

We investigate the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. We show that this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. We also address some outstanding issues with Wall's method, in particular, its gauge invariance and its relation to the Iyer-Wald entropy.