Gravitational instabilities of isothermal spheres in the presence of a cosmological constant. (English) Zbl 1262.83025
Summary: Gravitational instabilities of isothermal spheres are studied in the presence of a positive or negative cosmological constant, in the Newtonian limit. In gravity, the statistical ensembles are not equivalent. We perform the analysis both in the microcanonical and the canonical ensembles, for which the corresponding instabilities are known as ‘gravothermal catastrophe’ and ‘isothermal collapse’, respectively. In the microcanonical ensemble, no equilibria can be found for radii larger than a critical value, which is increasing with increasing cosmological constant. In contrast, in the canonical ensemble, no equilibria can be found for radii smaller than a critical value, which is decreasing with increasing cosmological constant. For a positive cosmological constant, characteristic reentrant behavior is observed.
MSC:
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
| 82B30 | Statistical thermodynamics |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
Keywords:
self-gravitating gas; gravothermal instability; cosmological constant; reentrant phase transitionReferences:
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