Schwarzschild solution as a result of thermodynamics

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-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.

two new authors joined, 5pages, no figure, PRD in press

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• Gravity is not an entropic force
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• Horizon entropy and higher curvature equations of state
• MOND cosmology from entropic force
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• First Principle Study of Gravitational Pressure and Thermodynamics of FRW Universe
• Black holes and gravitational waves in three-dimensional f(R) gravity
• The global monopole spacetime and its topological charge
• From thermodynamics to the solutions in gravity theory
• A modified thermodynamics method to generate exact solutions of the Einstein equations
• Dynamical spacetimes in conformal gravity
• Non perturbative spherical gravitational waves
• Quasilocal Smarr relations for static black holes
• Screen chaotic motion by Shannon entropy in curved spacetimes
• Implications of maximum acceleration on dynamics