Formation of naked singularities in five-dimensional space-time

Details Formation of naked singularities in five-dimensional space-time Formation of naked singularities in five-dimensional space-time

2011-02-10

arxiv.org/abs/1102.2090v1

Phys.Rev.D83:064006,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, 5 figures, To be published in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.83.064006

We numerically investigate the gravitational collapse of collisionless particles in spheroidal configurations both in four and five-dimensional (5D) space-time. We repeat the simulation performed by Shapiro and Teukolsky (1991) that announced an appearance of a naked singularity, and also find that the similar results in 5D version. That is, in a collapse of a highly prolate spindle, the Kretschmann invariant blows up outside the matter and no apparent horizon forms. We also find that the collapses in 5D proceed rapidly than in 4D, and the critical prolateness for appearance of apparent horizon in 5D is loosened compared to 4D cases. We also show how collapses differ with spatial symmetries comparing 5D evolutions in single-axisymmetry, SO(3), and those in double-axisymmetry, U(1)$\times$U(1).

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