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# Hoop conjecture in five dimensions: Violation of cosmic censorship

• ##### Daisuke Ida
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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ABSTRACT: We study the method for generating the initial data of black hole systems in Gauss-Bonnet (GB) gravity. The initial data are assumed to be momentarily static and conformally flat. Although the equation for the conformal factor is highly nonlinear, it is successfully solved by numerical relaxation for one-black-hole and two-black-hole systems. The common apparent horizon is studied in the two-black-hole initial data, and the result suggests that the Penrose inequalities are satisfied in this system. This is the first step for simulating black hole collisions in higher-curvature theories.
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ABSTRACT: We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2 or S**1 x S**3, which is a higher-dimensional generalization of the black ring.
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