Generalized Second Law for Non-minimally Coupled Matter Theories

TL;DR

This paper extends the proof of the generalized second law of thermodynamics to higher curvature gravity theories with non-minimally coupled matter, using an effective field theory approach in the linearized regime.

Contribution

It generalizes the linearized semi-classical GSL proof to include non-minimal matter couplings in higher curvature gravity theories.

Findings

Proof of GSL for non-minimally coupled matter in higher curvature gravity.

Method for evaluating matter path integrals with higher derivative couplings.

Validation of the second law in the linearized fluctuation regime.

Abstract

We prove the generalized second law (GSL) for higher curvature gravity theories when the matter sector is non-minimally coupled. The validity of our proof is in the regime of linearized fluctuations about equilibrium black holes, which is the same regime as considered in the previous proofs by Wall and Sarkar. These proofs were provided in different gravity theories - for instance, Lovelock theory and higher curvature gravity - but the matter sector was always taken to be minimally coupled. In this article, we describe how to generalize the proof of linearized semi-classical GSL when the matter sector comes with non-minimal couplings. The proof proceeds by suitably evaluating the matter path integral in the stress tensor expectation value by treating the higher derivative couplings in an effective field theory setting. We use the recently established result of the linearized second law for such theories.