Hoop Conjecture in Five-dimensios -Violation of Cosmic Censorship-

Abstract

We study the condition of black hole formation in five-dimensional space-time. We analytically solve the constraint equations of five-dimensional Einstein equations for momentarily static and conformally flat initial data of a spheroidal mass. We numerically search for an apparent horizon in various initial hypersurfaces and find both necessary and sufficient conditions for the horizon formation in terms of inequalities relating a geometric quantity and a mass defined in an appropriate manner. In the case of infinitely thin spheroid, our results suggest a possibility of naked singularity formation by the spindle gravitational collapse in five-dimensional space-time.

arXiv comment23 pages, 7 figures, PRD accepted version

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Cited by in corpus (8)

• Black Holes in Higher Dimensions
• Spherical gravitational collapse in N-dimensions
• Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture
• Formation of naked singularities in five-dimensional space-time
• Black Objects and Hoop Conjecture in Five-dimensional Space-time
• Hoop Conjecture and the Horizon Formation Cross-Section in Kaluza-Klein Spacetimes
• 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