The dimensional dependence of naked singularity formation in spherical gravitational collapse

The complete spectrum of the endstates-naked singularities or black holes-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 the black hole to the naked singularity can occur, is still present if N = 5 but does not occur if N > 5, independently of the initial data of the collapse. Physically, the results turn out to be related to the kinematical properties of the considered solutions.