Thermal equilibrium states and instability of self-gravitating particles in an asymptotically AdS spacetime

TL;DR

This paper studies the existence and stability of thermal equilibrium states of self-gravitating particles in asymptotically AdS spacetime, revealing finite mass solutions without artificial walls and analyzing their stability via turning point methods.

Contribution

It demonstrates that in asymptotically AdS spacetime, self-gravitating systems can have finite mass equilibria without artificial boundaries and explores their stability properties.

Findings

Finite mass equilibrium states exist without artificial walls in AdS spacetime.

Equilibrium states form a double spiral structure in parameter space.

Stability is analyzed using the turning point method, revealing restricted gravothermal energy regions.

Abstract

We investigate the existence and the stability of spherically symmetric thermal equilibrium states of the self-gravitating many-particle system which satisfies the Einstein-Vlasov equations with a negative cosmological constant. While a thermal equilibrium state of the self-gravitating particle system cannot have a finite mass without an artificial wall in the asymptotically flat case, in the asymptotically AdS case, the total mass can be finite without any artificial wall due to the AdS potential barrier. In this case, the typical size of the system is characterized by the AdS radius. The equilibrium states can be parametrized by two independent parameters. Taking the total rest mass as the unit and fixing the AdS radius, we obtain the one-parameter family of equilibria which describes a curve in the parameter space spanned by the gravothermal energy and the temperature. Then we investigate the instability of the system based on the turning point method for each value of the AdS radius. We find that the curve typically has a double spiral structure as in the asymptotically flat case with an artificial wall. The possible value of the gravothermal energy is restricted to the finite region between the first turning points on the two respective spirals.