Schwarzschild solution as a result of thermodynamics

TL;DR

This paper derives the Schwarzschild and other spherically symmetric solutions from thermodynamic principles, using the Misner-Sharp mass and geometric surface gravity, extending to various spacetime geometries.

Contribution

It presents a novel thermodynamic derivation of known solutions, emphasizing the role of the Misner-Sharp mass in spherically symmetric spacetimes.

Findings

Derivation of Schwarzschild solution from thermodynamics.

Extension to de Sitter, anti-de Sitter, Reissner-Nordström, and higher-dimensional spacetimes.

Highlighting the Misner-Sharp mass as an adiabatic system's mass.

Abstract

We obtain the Schwarzschild solution from thermodynamic considerations using the assumptions of a quasi local mass form (the Misner-Sharp mass) and geometric surface gravity in a spherically symmetric spacetime. The deduction is extended to other cases such as the de Sitter, anti-de Sitter, Reissner-Nordstr\"om and higher dimensional spacetimes. This paper demonstrates the simple hypotheses to obtain these known spherically symmetric solutions via thermodynamics, where essentially the Misner-Sharp mass is the mass for an adiabatic system.