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arXiv · 2306.11744

Kinetic formulation of Tolman-Ehrenfest effect: Non-ideal fluids in Schwarzschild and Kerr space-times

Claudio Cremaschini·Jiří Kovář·Zdeněk Stuchlík·Massimo Tessarotto
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Abstract

A review of the original thermodynamic formulation of the Tolman-Ehrenfest effect prescribing the temperature profile of uncharged fluid at thermal equilibrium forming stationary configurations in curved space-time is proposed. A statistical description based on relativistic kinetic theory is implemented. In this context the Tolman-Ehrenfest relation arises in the Schwarzschild space-time for collisionless uncharged particles at Maxwellian kinetic equilibrium. However, the result changes considerably when non-ideal fluids, i.e., non-Maxwellian distributions, are treated, whose statistical temperature becomes non-isotropic and gives rise to a tensor pressure. This is associated with phase-space anisotropies in the distribution function, occurring both for diagonal and non-diagonal metric tensors, exemplified by the Schwarzschild and Kerr metrics respectively. As a consequence, it is shown that for these systems it is not possible to define a Tolman-Ehrenfest relation in terms of an isotropic scalar temperature. Qualitative properties of the novel solution are discussed.

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Claudio Cremaschini, Jiří Kovář, Zdeněk Stuchlík, Massimo Tessarotto. 2023-06-17. Kinetic formulation of Tolman-Ehrenfest effect: Non-ideal fluids in Schwarzschild and Kerr space-times. https://doi.org/10.1063/5.0111200

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