Charis Anastopoulos, Ntina Savvidou
We prove that in any static spacetime the maximization of matter entropy subject to the continuity equation for the stress-energy tensor and the initial-value constraint leads to the full set of Einstein equations and to Tolman's relation between local temperature and lapse function. This result is shown to imply that the thermodynamics of gravitating systems in equilibrium is fully specified by variables defined on the system's boundary, in particular, the boundary's geometry and extrinsic curvature. Hence, self-gravitating systems in equilibrium are holographic already at the level of classical relativity.
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http://arxiv.org/abs/1302.4407
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