Kinetic formulation of Tolman-Ehrenfest effect: Non-ideal fluids in Schwarzschild and Kerr space-times
| Autor: | Cremaschini, Claudio, Kovář, Jiří, Stuchlík, Zdeněk, Tessarotto, Massimo |
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| Rok vydání: | 2023 |
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| Zdroj: | Physics of Fluids 34, 091701 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/5.0111200 |
| Popis: | 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. Comment: 7 pages. arXiv admin note: text overlap with arXiv:2306.10434 |
| Databáze: | arXiv |
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