Tolman-Ehrenfest's criterion of thermal equilibrium extended to conformally static spacetimes

Abstract

With insight from examples and physical arguments, the Tolman-Ehrenfest criterion of thermal equilibrium for test fluids in static spacetimes is extended to local thermal equilibrium in conformally static geometries. The temperature of the conformally rescaled fluid scales with the inverse of the conformal factor, reproducing the evolution of the cosmic microwave background in Friedmann universes and a heuristic argument by Dicke.