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arXiv · 2409.12861

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

Marcello Miranda·Massimiliano Rinaldi·Valerio Faraoni
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Abstract

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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Marcello Miranda, Massimiliano Rinaldi, Valerio Faraoni. 2024-09-19. How the Schwarzschild-de Sitter horizons remain in thermal equilibrium at vastly different temperatures. https://doi.org/10.1103/physrevd.110.104065

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