Abstract
We establish that boundary degrees of freedom associated with a generic codimension one null surface in $D$-dimensional pure Einstein gravity naturally admit a thermodynamical description. We expect the 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 of 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.
Highlights
Despite apparent differences, there are various hints that gravity, as formulated by Einstein’s general relativity (GR), and thermodynamics are closely related to each other, both at conceptual and formulation levels
We expect the 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
In the context of black hole physics the resemblance between laws of black hole mechanics and laws of thermodynamics [1] was gradually completed into the equivalence of the two [2–10]
Summary
There are various hints that gravity, as formulated by Einstein’s general relativity (GR), and thermodynamics are closely related to each other, both at conceptual and formulation levels. Black hole microstates may be sought among these boundary degrees of freedom With this motivation, we study gravity theory on spacetimes with a null boundary. We study gravity theory on spacetimes with a null boundary This boundary can be an arbitrary one in spacetime and is not necessarily horizon of a black hole. We construct the solution phase space governing the boundary degrees of freedom and show it can be naturally viewed as an open thermodynamic phase space This open thermodynamics system can be closed if we turn off the graviton flux passing through the null surface. The latter, together with an extra relation among the chemical potentials and associated surface charges (3.9), yields the statement of the local zeroth law. Our derivation only relies on diffeomorphism invariance of the theory and we expect our thermodynamical description to be true for any generally invariant theory of gravity
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