Numerical Investigations of Singularities in Higher-Dimensional Space-time

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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.