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Local approach to thermodynamics of black holes

E. Czuchry·J. Jezierski·J. Kijowski
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Abstract

Hamiltonian description of gravitational field contained in a spacetime region with boundary $S$ being a null-like hypersurface (a wave front) is discussed. Complete generating formula for the Hamiltonian dynamics (with no surface integrals neglected) is presented. A quasi-local proof of the 1-st law of black holes thermodynamics is obtained as a consequence, in case when $S$ is a non-expanding horizon. The 0-th law and Penrose inequalities are discussed from this point of view.

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E. Czuchry, J. Jezierski, J. Kijowski. 2004-05-14. Local approach to thermodynamics of black holes. https://arxiv.org/abs/gr-qc/0405073

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