论文标题
$ d $维度渐近性广告时空中的巨大灾难和临界维度
Gravothermal catastrophe and critical dimension in a $D$-dimensional asymptotically AdS spacetime
论文作者
论文摘要
我们研究了$ D $二维的渐近抗DE安慰剂（ADS）时空中球形对称自我赋入系统的热平衡状态的结构和稳定性。该系统满足了Einstein-Vlasov方程，具有负宇宙常数。由于ADS电位的狭窄结构，我们可以在渐近的ADS时空构建热平衡状态，而无需任何人造壁。因此，广告半径可以视为系统的典型尺寸。然后，系统可以以重生能量为特征，并由总颗粒数归一化的ADS半径。我们使用转弯点方法研究了系统在$ d $维时的灾难性不稳定。结果，我们发现曲线具有$ 4 \ le d \ le 10 $的双螺旋结构，而它没有任何螺旋结构，而没有任何螺旋结构，就像$ d \ ge11 $的螺旋结构一样，如被绝热墙所限制的渐近平面外壳。不论螺旋结构的存在如何，都存在重生能量的上限和下限。这一事实表明，在重生能量的允许区域之外没有热平衡溶液。该属性也类似于渐近平面案例。
We investigate the structure and stability of the thermal equilibrium states of a spherically symmetric self-gravitating system in a $D$-dimensional asymptotically Anti-de Sitter(AdS) spacetime. The system satisfies the Einstein-Vlasov equations with a negative cosmological constant. Due to the confined structure of the AdS potential, we can construct thermal equilibrium states without any artificial wall in the asymptotically AdS spacetime. Accordingly, the AdS radius can be regarded as the typical size of the system. Then the system can be characterized by the gravothermal energy and AdS radius normalized by the total particle number. We investigate the catastrophic instability of the system in a $D$-dimensional spacetime by using the turning point method. As a result, we find that the curve has a double spiral structure for $4\le D\le 10$ while it does not have any spiral structures for $D\ge11$ as in the asymptotically flat case confined by an adiabatic wall. Irrespective of the existence of the spiral structure, there exist upper and lower bounds for the value of the gravothermal energy. This fact indicates that there is no thermal equilibrium solution outside the allowed region of the gravothermal energy. This property is also similar to the asymptotically flat case.
