Null Surface Geometry and Associated Thermodynamics

Abstract

The emergent gravity paradigm interprets the gravitational field equations as describing the thermodynamic limit of the underlying statistical mechanics of the microscopic degrees of freedom associated with the spacetime structure. The connection is established by attributing a heat density to the null surfaces. The explicit form of the entropy functional determines the nature of the gravitational theory. We explore the consequences of this paradigm for an arbitrary null surface and highlight the key thermodynamic interpretations of various geometrical quantities. In particular, we show that: three distinct projections of gravitational momentum related to an arbitrary null surface in the spacetime lead to three different equations, all of which have thermodynamic interpretation. The first one reduces to a Navier-Stokes equation for the transverse drift velocity. The second can be written as a thermodynamic identity, while the third one describes the time evolution of the null surface in terms of suitably defined surface and bulk degrees of freedom.