Hoop conjecture in five dimensions: Violation of cosmic censorship

Department of Physics, Gakushuin University, 171-8588, Tokyo, Japan
Physical Review D (Impact Factor: 4.64). 04/2005; 71(10). DOI: 10.1103/PhysRevD.71.104014
Source: arXiv


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 investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general {\it type I} matter field, which is a broad class that includes most of the physically reasonable matter forms. We show that given the initial data for matter in terms of the initial density and pressure profiles at an initial surface $t=t_i$ from which the collapse evolves, there exist rest of the initial data functions and classes of solutions of Einstein equations which we construct here, such that the spacetime evolution goes to a final state which is either a black hole or a naked singularity, depending on the nature of initial data and evolutions chosen, and subject to validity of the weak energy condition. The results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics. The formalism here combines the earlier results on gravitational collapse in four dimensions in a unified treatment. Also the earlier work is generalized to higher dimensional spacetimes to allow a study of the effect of number of dimensions on the possible final outcome of the collapse in terms of either a black hole or naked singularity. No restriction is adopted on the number of dimensions, and other limiting assumptions such as self-similarity of spacetime are avoided, in order to keep the treatment general. Our methodology allows to consider to an extent the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.
    Physical review D: Particles and fields 09/2006; 76(8). DOI:10.1103/PHYSREVD.76.084026 · 4.86 Impact Factor
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    ABSTRACT: We review black hole solutions of higher-dimensional vacuum gravity, and of higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.
    Living Reviews in Relativity 01/2008; 11. DOI:10.12942/lrr-2008-6 · 19.25 Impact Factor
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    ABSTRACT: We analyze momentarily static initial data sets of the gravitational field produced by two-point sources in five-dimensional Kaluza-Klein spacetimes. These initial data sets are characterized by the mass, the separation of sources and the size of a extra dimension. Using these initial data sets, we discuss the condition for black hole formation, and propose a new conjecture which is a hybrid of the four-dimensional hoop conjecture and the five-dimensional hyperhoop conjecture. By using the new conjecture, we estimate the cross section of black hole formation due to collisions of particles in Kaluza-Klein spacetimes. We show that the mass dependence of the cross section gives us information about the size and the number of the compactified extra dimensions.
    Physical Review D 06/2009; DOI:10.1103/PhysRevD.81.024020 · 4.64 Impact Factor
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