Gravitational Entropy

TL;DR

This work addresses defining gravitational entropy without invoking temperature by recasting entropy as a Wald-like Noether charge in a covariant phase space that allows a configuration-space dependent generator tied to lightsheets. It introduces a necessary correction term for the vector field variation to maintain a consistent charge, then applies the formalism to Schwarzschild, Kerr, Kerr–Newman, de Sitter, and Kottler spacetimes, recovering the standard area law S = A/(4 G ħ) and the relevant first-law relations. The methodology unifies horizon and cosmological-geometry entropies under a single Noether-charge framework and highlights the role of boundary light-sheets in determining gravitational entropy. The results suggest a universal bound tied to boundary structure, with potential extensions to general spatial regions and higher-order quantum effects, while leaving the microscopic interpretation as an open question.

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.