Local temperature in general relativity

We examine the Tolman temperature by using Carter???s variational formalism of thermodynamics. We restrict our interests to fluids in thermal equilibrium that the heat does not propagate. We show that this condition presents a general formula for the local temperature gradient. We suggest a resolution of the recently addressed conflict in Tolman temperature when a chemical potential does not vanish.

Automated summary

In this study, we examine the Tolman temperature using Carter's variational formalism of thermodynamics. We focus on fluids in thermal equilibrium where heat does not propagate, and derive a general formula for the local temperature gradient under this condition. We propose a resolution for the conflict in Tolman temperature when a non-zero chemical potential is present.