Numerical Investigations of Singularities in Higher-Dimensional Space-time

我们利用数值模拟研究了高维时空中奇点和/或黑洞的形成过程。通过对引力坍缩的分析，我们发现(1)由于引力在高维时空中传播更自由，坍缩进行得更快，坍缩物质的构型更接近球形；(2)当物质处于高度纺锤形时，时间演化导致裸奇点的形成，但与四维情况相比，临界构型是松散的；(3)环形物质引力坍缩的黑环形成过程以及视界的拓扑变化。从摄动分析中，我们还发现ellis型虫洞解在任何维度时空中都是不稳定的。研究还包括提出在时间积分中对约束违反具有鲁棒性的爱因斯坦方程的公式。

We investigated formation process of singularities and/or black holes in higher-dimensional space-time using numerical simulations. From the analysis of gravitational collapses, we find (1) the collapse proceeds faster and the collapsing matter's configuration approaches more spherical, since gravity propagates with more freedom in higher-dimensional space-time; (2) if matter is in highly spindle shape, then the time evolution results in the formation of naked singularities, but the critical configuration is loosend compared with 4-dimensional cases; (3) the process of black-ring formation together with the topology change of the apparent horizon, for gravitational collapse of ring-shaped matter. From the perturbation analysis, we also find Ellis-type wormhole solutions are unstable in any dimensional space-time.The research also includes the proposals of formulation of the Einstein equations which is robust against constraint violations during time integrations.