Gravitational instabilities of isothermal spheres in the presence of a cosmological constant

TL;DR

This paper investigates how a cosmological constant influences gravitational instabilities in isothermal spheres, revealing ensemble-dependent behaviors and reentrant phenomena in the presence of positive cosmological constants.

Contribution

It provides a detailed analysis of gravitational instabilities considering the cosmological constant in both microcanonical and canonical ensembles, highlighting ensemble differences and reentrant behavior.

Findings

Microcanonical ensemble: no equilibria for radii larger than a critical value, increasing with the cosmological constant.

Canonical ensemble: no equilibria for radii smaller than a critical value, decreasing with the cosmological constant.

Reentrant behavior observed for positive cosmological constant.

Abstract

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 behaviour is observed.