Null Surface Thermodynamics in Topologically Massive Gravity

TL;DR

This paper explores null surface thermodynamics in three-dimensional topologically massive gravity, revealing boundary degrees of freedom obey local thermodynamic laws and describing an out-of-equilibrium open boundary system.

Contribution

It introduces a boundary degrees of freedom framework in TMG and formulates null surface thermodynamics with local laws, extending understanding of boundary dynamics in gravity.

Findings

Boundary degrees of freedom obey local thermodynamic laws.

Null surface thermodynamics includes a local first law, Gibbs-Duhem, and zeroth law.

The system is generally out of thermal equilibrium due to boundary expansion and bulk mode passage.

Abstract

We study three dimensional topologically massive gravity (TMG) in presence of a generic codimension one null boundary. The existence of the boundary is accounted for by enlarging the Hilbert space of the theory by degrees of freedom which only reside at the boundary, the boundary degrees of freedom. The solution phase space of this theory in addition to bulk massive chiral gravitons of the TMG, involves boundary modes which are labeled by surface charges associated with large diffeomorphisms. We show boundary degrees of freedom obey a local thermodynamic description over the solution phase space, null surface thermodynamics, described by a local version of the first law, a local Gibbs-Duhem equation, and local zeroth law. Due to the expansion of the boundary and also the passage of the bulk mode through the boundary, our null surface thermodynamics describes an open boundary system that is generically out of thermal equilibrium.