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Hoop conjecture in five dimensions: Violation of cosmic censorship

Department of Mathematics and Physics, Osaka City University; Department of Mathematics and Physics, Graduate School of Science, Osaka City University, 558-8585, Osaka, Japan; Department of Physics, Gakushuin University, 171-8588, Tokyo, Japan
Physical Review D (Impact Factor: 4.69). 04/2005; DOI: 10.1103/PhysRevD.71.104014
Source: arXiv

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 numer-ically 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.

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