Gravitational-thermodynamic instabilities of isothermal spheres in dS and AdS

TL;DR

This paper investigates how a cosmological constant influences the thermodynamical stability of fluid spheres in both Newtonian gravity and General Relativity, revealing stabilization effects and phase transitions related to de Sitter and anti-de Sitter spaces.

Contribution

It provides a comparative analysis of thermodynamical stability of fluid spheres with a cosmological constant in Newtonian and relativistic frameworks, highlighting stabilization and phase transition phenomena.

Findings

Increased cosmological constant stabilizes the system.

Reentrant phase transitions occur with positive cosmological constant.

Critical radius for instability exceeds black hole radius and reaches the cosmological horizon.

Abstract

Thermodynamical stability of fluid spheres is studied in the presence of a cosmological constant, both in the Newtonian limit, as well as in General Relativity. In all cases, an increase of the cosmological constant tends to stabilize the system, making asymptotically de Sitter space more thermodynamically stable than anti-de Sitter at the purely classical level. In addition, in the Newtonian case reentrant phase transitions are observed for a positive cosmological constant, due to its repelling property in this case. In General Relativity is studied the case of radiation, for which is found that the critical radius, at which an instability sets in, is always bigger than the black hole radius of the system and furthermore, at some value of the cosmological constant this critical radius hits at the cosmological horizon.