Null Surface Thermodynamics

Abstract

Formulating $D$ dimensional pure Einstein gravity in spacetimes with a null codimension one boundary requires addition of boundary degrees of freedom (BDOF) to the the usual bulk gravitons. We construct the solution space perturbatively around the null boundary in which BDOF are described by $D$ functions on the codimension one null boundary. Employing covariant phase space formalism we compute charges associated with symmetries which rotate us within the solution phase space. We establish that the system admit a thermodynamical description and that the null surface thermodynamics is a consequence of the diffeomorphism invariance of the theory, not relying on other special features of the null surface or the gravity theory. In presence of flux of bulk gravitons through the null boundary we deal with an open thermodynamical system. Our analysis here extends the usual laws of black hole thermodynamics in two ways: it is true for any null surface (which is not necessarily horizon of a black hole) which may describe a system out of thermal equilibrium and that they are local equations over the null surface.