Gravitational entropy

Abstract

We formulate the classical gravitational entropy of a horizon as a Noether charge that does not require the notion of a temperature, and which is applicable to horizons that are not necessarily associated with black holes. This introduces a correction to the covariant phase space formalism that accounts for the configuration-dependence of the generating vector field conjugate to the charge. The vector field is related to the proposal of Bousso that the gravitational entropy of a region is determined by the lightsheet at its boundary. We test the formula on various black hole and cosmological horizons.