Black Objects and Hoop Conjecture in Five-dimensional Space-time

Details Black Objects and Hoop Conjecture in Five-dimensional Space-time Black Objects and Hoop Conjecture in Five-dimensional Space-time

2009-07-15

arxiv.org/abs/0907.2570v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 10 figures Added a couple of comments and references, corrected grammatical errors. To be published in Class. Quant.

Scientific paper

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 horizons. We discussed when $S^3$ (black hole) or $S^1 \times S^2$ (black ring) horizons ("black objects") are formed. By monitoring the location of the maximum Kretchmann invariant, an appearance of `naked singularity' or `naked ring' under special situation 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.

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