Thermality and heat content of horizons from infinitesimal coordinate transformations

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 a uniformly accelerated frame can be used to obtain the heat content and entropy of the Rindler horizon. This result offers insight into the observer-dependent degrees of freedom which contribute to the entropy of null surfaces.