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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2020

Caloric curves of classical self-gravitating systems in general relativity

Résumé

We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter ν=GNm/Rc2, called the compactness parameter, where N is the particle number and R the system's size. Typically, the caloric curves have the form of a double spiral. The “cold spiral,” corresponding to weakly relativistic configurations, is a generalization of the caloric curve of nonrelativistic classical self-gravitating systems. The “hot spiral,” corresponding to strongly relativistic configurations, is similar (but not identical) to the caloric curve of the ultrarelativistic self-gravitating black-body radiation. We introduce two types of normalization of energy and temperature to obtain asymptotic caloric curves describing, respectively, the cold and the hot spirals in the limit ν→0. As the number of particles increases, the cold and the hot spirals approach each other, merge at νS′=0.128, form a loop above νS=0.1415, reduce to a point at νmax=0.1764, and finally disappear. Therefore, the double spiral shrinks when the compactness parameter ν increases, implying that general relativistic effects render the system more unstable. We discuss the nature of the gravitational collapse at low and high energies with respect to a dynamical (fast) or a thermodynamical (slow) instability. We also provide an historical account of the developments of the statistical mechanics of classical self-gravitating systems in Newtonian gravity and general relativity.

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Dates et versions

hal-02309050 , version 1 (08-10-2019)

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Giuseppe Alberti, Pierre-Henri Chavanis. Caloric curves of classical self-gravitating systems in general relativity. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2020, 101 (5), pp.052105. ⟨10.1103/PhysRevE.101.052105⟩. ⟨hal-02309050⟩
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