Generalized Second Law of Thermodynamics in Extended Theories of Gravity

TL;DR

This paper demonstrates that the generalized second law of thermodynamics remains valid in extended gravity theories like Gauss-Bonnet and Lovelock gravity by analyzing the apparent horizon of a FRW universe as a thermal system.

Contribution

It extends the validity of the generalized second law to Gauss-Bonnet and Lovelock gravity using a thermodynamic approach on the apparent horizon.

Findings

The generalized second law holds in Gauss-Bonnet gravity.

The law also holds in Lovelock gravity.

Thermodynamic equilibrium is assumed for the horizon region.

Abstract

By employing the general expression of temperature $T_{h}=|\kappa|/2\pi = \frac{1}{2\pi \tilde{r}_{A}}(1-\frac{\dot{\tilde{r}}_{A}}{2H\tilde{r}_{A}})$ associated with the apparent horizon of a FRW universe and assuming a region of FRW universe enclosed by the apparent horizon as a thermal system in equilibrium, we are able to show that the generalized second law of thermodynamics holds in Gauss-Bonnet gravity and in more general Lovelock gravity.