We investigate the existence and the stability of spherically symmetric thermal equilibrium states of the self-gravitating many-particle system that 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 due to the AdS potential barrier without any artificial wall. In this case, the AdS radius characterizes the typical size of the system. The two independent parameters parametrize the equilibrium states. 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 equilibrium solutions exist only for the finite parameter region of the gravothermal energy between the onsets of the spirals.

我们研究了自引力多粒子系统的球对称热平衡状态的存在性和稳定性，该系统满足具有负宇宙常数的爱因斯坦-弗拉索夫方程。在渐近平坦的情况下，自引力粒子系统的热平衡状态在没有人造墙的情况下不能具有有限质量，而在渐近 AdS 情况下，由于没有任何人造墙的 AdS 势垒，总质量可以是有限的。在这种情况下，AdS 半径表征了系统的典型大小。两个独立的参数参数化平衡状态。以总静止质量为单位，固定 AdS 半径，我们获得了单参数平衡族，它描述了重力热能和温度所跨越的参数空间中的曲线。然后我们基于 AdS 半径的每个值的转折点法研究系统的不稳定性。我们发现曲线通常具有双螺旋结构，就像在带有人造墙的渐近平坦情况下一样。平衡解只存在于螺旋起始点之间重力热能的有限参数区域。