Thermal nature of a generic null surface

TL;DR

This paper demonstrates that a null surface can be assigned a meaningful temperature for a local observer, based on quantum effects and an analogy with thermodynamics, highlighting its physical relevance.

Contribution

It materializes the analogy between thermodynamics and gravitational field equations on null surfaces, establishing a physical basis for assigning temperature to such surfaces.

Findings

A local observer perceives a finite temperature near the null surface.

Quantum probability of escape follows a Maxwell-Boltzmann distribution.

Null surfaces exhibit thermodynamic properties with physical significance.

Abstract

Dynamical properties of a generic null surface are known to have a thermodynamic interpretation. Such an interpretation is completely based on an analogy between the usual law of thermodynamics and structure of gravitational field equation on the surface. Here we materialise this analogy and show that assigning a temperature on the null surface for a local observer is indeed physically relevant. We find that for a local frame, chosen as outgoing massless chargeless particle (or field mode), perceives a "{\it local unstable Hamiltonian}" very near to the surface. Due to this it has finite quantum probability to escape through acausal null path which is given by Maxwell-Boltzmann like distribution, thereby providing a temperature on the surface.