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

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 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.

20 pages, 10 figures Added a couple of comments and references, corrected grammatical errors. To be published in Class. Quant. Grav. (2010)

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• Black Holes in Higher Dimensions
• Black Saturn
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• A Reformulation of the Hoop Conjecture
• $N+1$ formalism in Einstein-Gauss-Bonnet gravity
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Cited by in corpus (6)

• More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons
• Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture
• Formation of naked singularities in five-dimensional space-time
• Nonlinear Dynamics in the Einstein-Gauss-Bonnet gravity
• Black hole initial data in Gauss-Bonnet gravity: Momentarily static case
• Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times