Dimensional dependence of naked singularity formation in spherical gravitational collapse

TL;DR

This paper investigates how the dimension of spacetime influences the endstates of gravitational collapse, revealing a critical behavior at four dimensions that changes for higher dimensions, affecting the formation of naked singularities or black holes.

Contribution

It generalizes previous collapse models to N-dimensional spacetimes and uncovers the dimensional dependence of critical phenomena in gravitational collapse.

Findings

Critical behavior at N=4 dimensions with phase transition from black hole to naked singularity.

No critical behavior for N>5, regardless of initial conditions.

Final collapse outcome depends on local scalar function and spacetime dimension.

Abstract

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.