# Symmetric Space-times from Thermodynamics

## TL;DR

This paper introduces a thermodynamics-based method to generate exact symmetric spacetime solutions in Einstein's equations, revealing relationships among various symmetric spacetimes and suggesting extensions to more complex cases.

## Contribution

It presents a novel thermodynamics approach to derive symmetric solutions without direct solving, linking different spacetime families and proposing new perspectives on Misner-Sharp mass.

## Key findings

- Generated known symmetric solutions using thermodynamics
- Identified relationships among plane, spherical, and pseudo-spherical spacetimes
- Extended insights to Kerr and Taub-NUT spacetimes

## Abstract

We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions are discussed in different situation. These results suggest that plane,spherical,pseudo-spherical symmetric spacetime form a family of solutions, and this relationship can also be extended to Kerr spacetime and Taub-NUT spacetime. It sheds light on exploring more general definition of Misner-Sharp mass.