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

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.

Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

“…(We will, however, briefly touch on related considerations [64][65][66][67][68][69][70][71][72] within the topic of gravitational dynamics in AdS outside spherical symmetry.) (c) Studies of the Einstein-Vlasov system in AdS [73,74] where powerful instability results have been obtained in [73] at a mathematically rigorous level. We note, however, that the dynamical realization of this instability is rather different from the classical field systems treated in [8] and the extensive follow-up work, nor is there a direct contact with the conventional approaches to the AdS/CFT correspondence.…”

Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

“…3. Studies of the Einstein-Vlasov system in AdS [71,72] where powerful instability results have been obtained in [71] at a mathematically rigorous level. We note, however, that the dynamical realization of this instability is rather different from the classical field systems treated in [7] and the extensive follow-up work, nor is there a direct contact with the conventional approaches to the AdS/CFT correspondence.…”