An entropy current for dynamical black holes in four-derivative theories of gravity

TL;DR

This paper introduces a local entropy current for dynamical black holes in four-derivative gravity theories, extending the second law of thermodynamics to dynamical, higher-derivative contexts.

Contribution

It presents a novel, local formulation of the second law for dynamical black holes in four-derivative gravity theories, including a general algorithm for constructing the entropy current.

Findings

Constructed a local entropy current for dynamical black holes.

Extended the second law to higher derivative gravity theories.

Provided an algorithm for entropy current construction with potential ambiguities.

Abstract

We propose an entropy current for dynamical black holes in a theory with arbitrary four derivative corrections to Einstein's gravity, linearized around a stationary black hole. The Einstein-Gauss-Bonnet theory is a special case of the class of theories that we consider. Within our approximation, our construction allows us to write down a completely local version of the second law of black hole thermodynamics, in the presence of the higher derivative corrections considered here. This ultra-local, stronger form of the second law is a generalization of a weaker form, applicable to the total entropy, integrated over a compact `time-slice' of the horizon, a proof of which has been recently presented in arXiv:1504.08040. We also provide a general algorithm to construct the entropy current for the four derivative theories, which may be straightforwardly generalized to arbitrary higher derivative corrections to Einstein's gravity. This algorithm highlights the possible ambiguities in defining the entropy current.