Abstract
The notion of thermal time has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we study this notion in the restricted context of stationary spacetimes. We show that the Tolman–Ehrenfest effect (in a stationary gravitational field, temperature is not constant in space at thermal equilibrium) can be derived very simply by applying the equivalence principle to a key property of thermal time; at equilibrium, temperature is the rate of thermal time with respect to proper time—the ‘speed of (thermal) time’. Unlike other published derivations of the Tolman–Ehrenfest relation, this one is free from any further dynamical assumption, thereby illustrating the physical import of the notion of thermal time.
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