The second law of black hole mechanics in effective field theory

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.

Automated summary

This article investigates the second law of black hole mechanics in gravitational theories with higher derivative terms. The author describes a method for defining an entropy that satisfies the second law to linear and quadratic orders in perturbations, treating the higher derivative terms as effective field theory. Additionally, the author addresses some outstanding issues with the method, such as gauge invariance and its relation to the Iyer-Wald entropy.