A modified thermodynamics method to generate exact solutions of the Einstein equations

TL;DR

This paper introduces a modified thermodynamics-based method using Komar and ADM masses to derive exact solutions of Einstein equations, including black holes with quintessence and monopole spacetimes.

Contribution

The authors develop a new approach that replaces Misner-Sharp energy with Komar and ADM masses, enabling the derivation of various Einstein solutions, including generalized monopole spacetimes.

Findings

Derived black hole solutions surrounded by quintessence.

Defined geometry surface gravity via Komar mass.

Generalized method to include monopole spacetimes.

Abstract

We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy which is used in the original methods, and then several exact solutions of Einstein equations are obtained, including the black hole solution which surrounded by quintessence. Moreover, the geometry surface gravity defined by Komar mass is obtained. Secondly, we use both the Komar mass and the ADM mass to modify such method, and the similar results are obtained. Moreover, with some generalize added to the definition of the ADM mass, our method can be generalized to global monopole sapcetime.