NUMERICAL STUDY OF FIVE-DIMENSIONAL GRAVITATIONAL COLLAPSES

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Five-dimensional black-hole and black-ring formation are investigated numerically. We model the initial matter distribution in homogeneous spheroidal and toroidal configurations under the momentarily static assumption and express the matter with collisionless particles. Evolutions of space-time and particles are followed by using ADM formalism (4 + 1 decomposition) and solving the geodesic equation. For spheroidal configurations, we repeat the simulation performed by Shapiro and Teukolsky (1991) that announced an appearance of a naked singularity, and also find similar results in the 5D version. For toroidal configurations in U(1)× U(1) symmetry, we consider the rotating collisionless particles which consist of equal numbers co-rotating and counter-rotating under a certain rotational law. We search both spherical(S) and ring-shaped(S × S) horizons, and show topology change of apparent horizon from ring-shaped to spherical shape during its evolution. We also discuss whether an observer at the origin of the ring-horizon can escape out or not.

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