Gravitational entropy and thermodynamics away from the horizon

TL;DR

This paper introduces a new invariant gravitational entropy defined via geometric integrals over spherical shells, extending thermodynamic concepts beyond horizons and linking them to dual field theories.

Contribution

It proposes a novel geometric definition of gravitational entropy applicable away from horizons, connecting it with thermodynamics and field theory duals.

Findings

The new entropy reduces to Wald's entropy at horizons.

Field theory duals of entropy, energy, and pressure match gravitational quantities.

Einstein equations correspond to thermodynamic relations in this framework.

Abstract

We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are 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.