The Tolman-Ehrenfest criterion for the thermal equilibrium of a fluid at rest in a static general-relativistic geometry is generalized to scalar-tensor gravity. The gravitational scalar field, which fixes the strength of the effective gravitational coupling, plays a role in determining thermal equilibrium. As a result, heat sinks more in a gravitational field where the geometry is more curved, but also where gravity is stronger.
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Karolinski et al. (2024) studied this question.
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