From thermodynamics to the solutions in gravity theory

TL;DR

This paper explores deriving solutions in various gravity theories using thermodynamic principles, extending previous work to modified theories like Gauss-Bonnet and $F(R)$ gravity, resulting in new solutions and insights.

Contribution

It generalizes the thermodynamic approach to find solutions in modified gravity theories, including a new class of solutions in $F(R)$ gravity.

Findings

Reproduces Boulware-Deser-Cai solution in Gauss-Bonnet gravity.

Derives a new class of solutions in $F(R)$ gravity with maximally symmetric subspaces.

Extends previous 3D black hole solutions to higher dimensions.

Abstract

In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the \sch~solution through thermodynamic laws by the aid of the Misner-Sharp mass in an adiabatic system. In this paper we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner-Sharp mass is the mass for an adiabatic system, we reproduce the Boulware-Deser-Cai solution in Guass-Bonnet gravity. Using this gravi-thermodynamics thought, we obtain a NEW class of solution in $F(R)$ gravity in an $n$-dimensional (n$\geq$3) spacetime which permits three-type $(n-2)$-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton-Barrow solution in $F(R)$ gravity.