Thermality and Heat Content of horizons from infinitesimal coordinate transformations

TL;DR

This paper demonstrates that the thermality and heat content of horizons can be derived from infinitesimal coordinate transformations between different reference frames, providing new insights into observer-dependent horizon entropy.

Contribution

It introduces a novel approach using infinitesimal coordinate transformations to derive horizon thermodynamics, linking observer dependence to horizon entropy.

Findings

Infinitesimal transformations reproduce known horizon thermodynamics.

The method applies to a wide class of geometries.

Provides insight into observer-dependent degrees of freedom.

Abstract

Thermal properties of a static horizon, (like the entropy S, heat content TS etc.) can be obtained either from the surface term of the Einstein-Hilbert action or by evaluating the Noether charge, corresponding to the diffeomorphisms generated by the timelike Killing vector field. We show that, for a wide class of geometries, the same results can be obtained using the vector field which produces an infinitesimal coordinate transformation between two physically relevant reference frames, viz. the freely falling frame near the horizon and the static, accelerated, frame. In particular, the infinitesimal coordinate transformation from inertial coordinates to uniformly accelerated frame can be used to obtain the heat content and entropy of the Rindler horizon. This result offers insight into understanding the observer dependent degrees of freedom which contribute to the entropy of null surfaces.