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• W2970208049 abstract "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 $ensuremath{nu}=GNm/R{c}^{2}$, 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 $ensuremath{nu}ensuremath{rightarrow}0$. As the number of particles increases, the cold and the hot spirals approach each other, merge at ${ensuremath{nu}}_{S}^{ensuremath{'}}=0.128$, form a loop above ${ensuremath{nu}}_{S}=0.1415$, reduce to a point at ${ensuremath{nu}}_{mathrm{max}}=0.1764$, and finally disappear. Therefore, the double spiral shrinks when the compactness parameter $ensuremath{nu}$ 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." @default.
• W2970208049 created "2019-09-05" @default.
• W2970208049 creator A5007478460 @default.
• W2970208049 creator A5083882693 @default.
• W2970208049 date "2020-05-11" @default.
• W2970208049 modified "2023-10-12" @default.
• W2970208049 title "Caloric curves of classical self-gravitating systems in general relativity" @default.
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