Thermodynamics on the apparent horizon in generalized gravity theories

TL;DR

This paper develops a general method to formulate the first law of thermodynamics on the apparent horizon within various extended gravity theories, including braneworld and Lovelock gravity, linking thermodynamics and gravitational dynamics.

Contribution

It introduces a unified procedure to derive the first law of thermodynamics on the apparent horizon applicable to multiple extended gravity models.

Findings

Validates the thermodynamic description in Randall-Sundrum braneworlds

Derives a generalized Misner-Sharp mass in Lovelock gravity

Establishes a link between Friedmann equations and thermodynamics

Abstract

We present a general procedure to construct the first law of thermodynamics on the apparent horizon and illustrate its validity by examining it in some extended gravity theories. Applying this procedure, we can describe the thermodynamics on the apparent horizon in Randall-Sundrum braneworld imbedded in a nontrivial bulk. We discuss the mass-like function which was used to link Friedmann equation to the first law of thermodynamics and obtain its special case which gives the generalized Misner-Sharp mass in Lovelock gravity.