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arxiv: 1304.3647 · v2 · submitted 2013-04-09 · 🌀 gr-qc · astro-ph.CO· hep-th· math-ph· math.MP

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Schwarzschild solution as a result of thermodynamics

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classification 🌀 gr-qc astro-ph.COhep-thmath-phmath.MP
keywords massmisner-sharpobtainschwarzschildsittersolutionsphericallysymmetric
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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.

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