Schwarzschild solution as a result of thermodynamics

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-Nordström 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.

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