Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas
Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
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Accepted: 21 February 2020
Published online: 16 March 2020
We study the statistical mechanics of classical self-gravitating systems confined within a box of radius R in general relativity. It has been found that the caloric curve has the form of a double spiral whose shape depends on the compactness parameter (Roupas in Class Quantum Grav 32:135023, 2015; Alberti and Chavanis in arXiv:1908.10316). The double spiral shrinks as increases and finally disappears when . Therefore, general relativistic effects render the system more unstable. On the other hand, the cold spiral and the hot spiral move away from each other as decreases. Using a normalization and appropriate to the nonrelativistic limit, and considering , the hot spiral goes to infinity and the caloric curve tends to a limit curve (determined by the Emden equation) exhibiting a single cold spiral, as found in former works. Using another normalization and appropriate to the ultrarelativistic limit, and considering , the cold spiral goes to infinity and the caloric curve tends to a limit curve (determined by the general relativistic Emden equation) exhibiting a single hot spiral. This result is new. We discuss the analogies and the differences between this asymptotic caloric curve and the caloric curve of the self-gravitating black-body radiation. Finally, we compare box-confined isothermal models with heavily truncated isothermal distributions in Newtonian gravity and general relativity.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020