https://doi.org/10.1140/epjp/s13360-020-00291-1
Regular Article
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
* e-mail: chavanis@irsamc.ups-tlse.fr
Received:
7
October
2019
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
