Expanding the Area of Gravitational Entropy

TL;DR

This work argues that gravitational entropy can be understood through the Gibbs-Duhem relation, with entropy $S$ arising from the gravitational heat $U-F$ and the equilibrium temperature $\beta^{-1}$ determined by Euclidean regularity. A quasilocal, counterterm-enhanced framework is developed to compute finite total energy, free energy, and entropy for a broad class of spacetimes, including those with cosmological horizons and nonzero NUT charge, without recourse to background subtraction. The approach connects to holography via universal boundary counterterms and demonstrates consistent entropy results for Schwarzschild–AdS, Taub-NUT–AdS, and de Sitter spacetimes, while highlighting deviations from the area law in nontrivial geometries. Open questions remain about the statistical mechanics underpinning gravitational entropy and the precise interpretation of these thermodynamic quantities in exotic spacetimes, as well as experimental tests.

Abstract

I describe how gravitational entropy is intimately connected with the concept of gravitational heat, expressed as the difference between the total and free energies of a given gravitational system. From this perspective one can compute these thermodyanmic quantities in settings that go considerably beyond Bekenstein's original insight that the area of a black hole event horizon can be identified with thermodynamic entropy. The settings include the outsides of cosmological horizons and spacetimes with NUT charge. However the interpretation of gravitational entropy in these broader contexts remains to be understood.