Gravitational entropy and thermodynamics away from the horizon

Details Gravitational entropy and thermodynamics away from the horizon Gravitational entropy and thermodynamics away from the horizon

2012-01-27

arxiv.org/abs/1201.5754v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages

Scientific paper

We define, by an integral over a spherical shell, an invariant geometric entropy of a black brane in an asymptotically anti-de Sitter spacetime. This gravitational entropy can be formulated on a shell of arbitrary radius and reduces to Wald's Noether charge entropy at the horizon of the black brane. We give the entropy a thermodynamic interpretation by similarly defining a gravitational energy and pressure and support this interpretation by showing that, for some specific cases, the field theory duals of the entropy, energy and pressure are indeed the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state.

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