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

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arxiv 2301.09021 v2 pith:J2VZ2W4H submitted 2023-01-21 gr-qc

Valerio Faraoni , Robert Vanderwee (Bishop's University) This is my paper · ORCID
classification gr-qc
keywords conformallyequilibriumstaticthermalcriterionextendedspacetimestemperature
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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, the Hawking temperature of the Sultana-Dyer cosmological black hole, and a heuristic argument by Dicke.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Thermodynamic parameters of fluids on conformally connected spacetimes

    gr-qc 2025-05 conditional novelty 6.0 of 10

    For conformally related Einstein spacetimes, equilibrium fluid temperature and chemical potential both scale as the inverse conformal factor, preserving the ratio μ/T.

  2. General relativistic heat flow from first order hydrodynamics

    gr-qc 2024-12 conditional novelty 5.0 of 10

    For non-viscous fluids in normal flow on static or stationary spacetimes, the redshifted heat current is conserved and the redshifted temperature obeys a curved-space Laplace-type heat equation.

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