Symmetric Space-times from Thermodynamics

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.