| Black Objects and Hoop Conjecture in Five-dimensional Space-time (2009) | |||||||||
Abstract | |||||||||
| We numerically investigated the sequences of initial data of thin spindle and thin ring in five-dimensional space-time in the context of the cosmic censorship conjecture. We modeled the matter in non-rotating homogeneous spheroidal or toroidal configurations under the momentarily static assumption, solved the Hamiltonian constraint equation, and searched the apparent horizon. We found both $S^3$ (black hole) and $S^2\times S^1$ (black ring) horizons ("black objects"), only when the matter configuration is not sharp. By monitoring the location of the maximum Kretchmann invariant, an appearance of `naked singularity' or `naked ring' under the special situations is suggested. We also discuss the validity of the {\it hyper-hoop} conjecture using minimum {\it area} around the object, and show that the appearance of the ring horizon does not match with this hoop.. Comment: 10 pages, 10 figures | |||||||||
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