Entropy of the gravitational field

Abstract

We develop a formulation of the entropy of the gravitational field by adopting the statistical mechanics expression for entropy S = lnΩ, where Ω is the phase space of the field bounded by a Hamiltonian. Phase space is calculated for gravitational waves and radiation and density perturbations in expanding FLRW spacetimes, attributing entropy to a lack of knowledge in the exact field configuration. In all cases, S behaves monotonically as required for a definition of gravitational entropy and is a good measure of inhomogeneity. It also reduces to black-hole entropy under appropriate circumstances.