论文标题
$ \ text {ads} _5 $中的Einstein-Vlasov系统具有等量角动量
Einstein-Vlasov system with equal-angular momenta in $\text{AdS}_5$
论文作者
论文摘要
我们调查了$ 5 $ - 尺寸旋转的爱因斯坦 - 弗拉索夫系统的解决方案，该系统具有$ r \ times su（2）\ times u（1）$ ismetry group。在五维时空中，有两个独立的旋转平面，因此，考虑到每个旋转平面上的$ u（1）$对称性，我们可能会将$ r \ times u（1）\ times u（1）\ times u（1）$等轴测施加到固定的时空。此外，当两个角动量的值彼此相等时，空间对称性将增强到$ r \ times su（2）\ times \ times u（1）$对称性，并且时空具有共振体1结构。将vlasov系统组成的粒子的分布函数施加相同的对称性，分布函数可以取决于粒子运动的三个相互独立和交换保守的电荷（能量，$ su（2）$（2）$和$ u（1）$角动量的总角动量）。我们考虑分布函数，该分布函数呈指数依赖于$ u（1）$角动量，并降低到球形对称性中的热平衡状态。然后，在本文中，我们在数值上构建了渐近广告爱因斯坦 - vlasov系统的解决方案。
We investigate solutions of the $5$--dimensional rotating Einstein-Vlasov system with an $R \times SU(2) \times U(1)$ isometry group. In a five-dimensional spacetime, there are two independent planes of rotation, thus, considering $U(1)$ symmetry on each rotation plane, we may impose an $R\times U(1) \times U(1)$ isometry to a stationary spacetime. Furthermore, when the values of the two angular momenta are equal to each other, the spatial symmetry gets enhanced to $R\times SU(2)\times U(1)$ symmetry, and the spacetime has a cohomogeneity-1 structure. Imposing the same symmetry to the distribution function of the particles of which the Vlasov system consists, the distribution function can be dependent on three mutually independent and commutative conserved charges for particle motion (energy, total angular momentum on $SU(2)$ and $U(1)$ angular momentum). We consider the distribution function which exponentially depends on the $U(1)$ angular momentum and reduces to the thermal equilibrium state in spherical symmetry. Then, in this paper, we numerically construct solutions of the asymptotically AdS Einstein--Vlasov system.
