1201.5754 (Ram Brustein et al.)

Gravitational entropy and thermodynamics away from the horizon    [PDF]

Ram Brustein, A. J. M. Medved

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.

View original: http://arxiv.org/abs/1201.5754