Local temperature in general relativity

TL;DR

This paper investigates the Tolman temperature in general relativity using Carter's thermodynamic formalism, deriving a general temperature gradient formula and addressing conflicts related to chemical potential.

Contribution

It introduces a new approach to understanding the Tolman temperature by applying Carter's formalism and resolves recent issues concerning non-vanishing chemical potential.

Findings

Derived a general formula for local temperature gradient in equilibrium

Resolved conflicts in Tolman temperature related to chemical potential

Provided insights into thermodynamics of fluids in curved spacetime

Abstract

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.