Formation of naked singularities in five-dimensional space-time

TL;DR

This study numerically explores gravitational collapse in 4D and 5D space-times, revealing conditions under which naked singularities form and how collapse dynamics differ with dimensionality and symmetry.

Contribution

It extends previous 4D collapse simulations to 5D, demonstrating naked singularity formation and analyzing effects of dimensionality and symmetry on collapse outcomes.

Findings

Naked singularities can form in 5D collapse similar to 4D.

Collapse in 5D proceeds faster than in 4D.

Looser conditions for apparent horizon formation in 5D.

Abstract

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).