Dimensional dependence of naked singularity formation in spherical gravitational collapse

Details Dimensional dependence of naked singularity formation in spherical gravitational collapse Dimensional dependence of naked singularity formation in spherical gravitational collapse

2007-07-11

arxiv.org/abs/0707.1608v2

Class.Quant.Grav.25:145003,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, to appear with minor modifications on Class. Quantum Grav

Scientific paper

10.1088/0264-9381/25/14/145003

The complete spectrum of the endstates - naked singularities, or blackholes - of gravitational collapse is analyzed for a wide class of $N$-dimensional spacetimes in spherical symmetry, which includes and generalizes the dust solutions and the case of vanishing radial stresses. The final fate of the collapse is shown to be fully determined by the local behavior of a single scalar function and by the dimension $N$ of the spacetime. In particular, the ``critical'' behavior of the N=4 spacetimes, where a sort of phase transition from black hole to naked singularity can occur, is still present if N=5 but does not occur if $N > 5$, independently from the initial data of the collapse. Physically, the results turn out to be related to the kinematical properties of the considered solutions.

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