Null Surface Thermodynamics

TL;DR

This paper demonstrates that null surfaces in Einstein gravity inherently possess a thermodynamic description, extending black hole thermodynamics to any null surface and highlighting its universal nature due to diffeomorphism invariance.

Contribution

It formulates laws of null surface thermodynamics using surface charge analysis, establishing a universal, local thermodynamic framework for arbitrary null surfaces in Einstein gravity.

Findings

Null surfaces admit a thermodynamic description derived from diffeomorphism invariance.

The laws of null surface thermodynamics are formulated as local equations.

The thermodynamic system is generally open, closing only without graviton flux.

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.