Gravothermal instability with a cosmological constant in the canonical ensemble

TL;DR

This paper investigates how a cosmological constant alters gravothermal instability in the canonical ensemble, revealing a reentrant phase transition and critical temperature behaviors.

Contribution

It extends the understanding of gravothermal instability by analyzing the effects of a cosmological constant within the canonical ensemble, highlighting new stability criteria and phase transitions.

Findings

Existence of a minimum radius for metastable states that decreases with the cosmological constant.

Identification of a second critical temperature leading to reentrant phase transitions.

Critical temperatures merge when the cosmological density is half the system's mean density.

Abstract

We present here how the gravothermal or Antonov's instability, which was originally formulated in the microcanonical ensemble, is modified in the presence of a cosmological constant and in the canonical ensemble. In contrast to the microcanonical ensemble, there is a minimum, and not maximum, radius for which metastable states exist. In addition this critical radius is decreasing, and not increasing, with increasing cosmological constant. The minimum temperature for which metastable states exist is decreasing with increasing cosmological constant, while above some positive value of the cosmological constant, there appears a second critical temperature. For lower temperatures than the second critical temperature value, metastable states reappear, indicating a typical reentrant phase transition. The two critical temperatures merge when the cosmological density equals one half the mean density of the system.