Null Surface Thermodynamics

TL;DR

This work establishes a universal framework in which the boundary degrees of freedom on a generic null surface in $D$-dimensional Einstein gravity admit a local thermodynamic interpretation. By leveraging the covariant phase space formalism and surface charges, it derives a local first law, a local extended Gibbs–Duhem equation, and a local zeroth law for open thermodynamic systems tied to graviton flux through the null boundary, with a clear separation between boundary and bulk data. The null boundary thermodynamic phase space comprises a thermodynamic sector, a flux-carrying $P$ sector, and bulk modes, with the expansion $\Theta$ tracking out-of-equilibrium effects; the framework reduces to standard black hole thermodynamics in appropriate limits and remains valid even out of equilibrium. The results generalize the gravity–thermodynamics correspondence beyond horizons, offering potential insights for the membrane paradigm and black hole microstates, and suggesting a path toward quantum boundary degrees of freedom and information considerations.

Abstract

We establish that boundary degrees of freedom associated with a generic co-dimension one null surface in $D$ dimensional pure Einstein gravity naturally admit a thermodynamical description. We expect the $\textit{null surface thermodynamics}$ to universally follow as a result of the diffeomorphism invariance of the theory, not relying on other special features of the null surface or the gravity theory. Using standard surface charge analysis and covariant phase space method, we formulate laws of null surface thermodynamics which are local equations over an arbitrary null surface paralleling local versions the zeroth and first laws and the Gibbs-Duhem equation. This thermodynamical system is generally an open system and can be closed only when there is no flux of gravitons through the null surface. Our analysis extends the usual black hole thermodynamics to a universal feature of any area element on a generic null surface. We discuss the relevance of our study for the membrane paradigm and black hole microstates.