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How the Schwarzschild-de Sitter horizons remain in thermal equilibrium at vastly different temperatures

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arxiv 2409.12861 v2 pith:ONVJYO4T submitted 2024-09-19 gr-qc

Marcello Miranda , Massimiliano Rinaldi , Valerio Faraoni This is my paper · ORCID
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keywords equilibriumhorizonsstaticthermalcriterionfluidgeneralizedradiation
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The Tolman-Ehrenfest criterion of thermal equilibrium for a static fluid in a static spacetime is generalized to stationary heat conduction, in the approximation in which backreaction is negligible. Applying this generalized criterion to the Hawking radiation in the Schwarzschild-de Sitter geometry shows that the two horizons (which act as thermostats) remain in thermal equilibrium. The temperature of the radiation fluid interpolates between the temperatures at the horizons, with a static analytic profile that is given explicitly.

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  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.

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