Hoop Conjecture in Five-dimensios -Violation of Cosmic Censorship-

TL;DR

This paper investigates black hole formation conditions in five-dimensional spacetime, revealing potential violations of cosmic censorship through numerical and analytical methods, especially in spindle gravitational collapse scenarios.

Contribution

It provides analytical solutions and numerical criteria for apparent horizon formation in five dimensions, highlighting conditions that may lead to naked singularities.

Findings

Necessary and sufficient conditions for horizon formation identified

Potential for naked singularity formation in spindle collapse

Analytical and numerical methods combined for analysis

Abstract

We study the condition of black hole formation in five-dimensional space-time. We analytically solve the constraint equations of five-dimensional Einstein equations for momentarily static and conformally flat initial data of a spheroidal mass. We numerically search for an apparent horizon in various initial hypersurfaces and find both necessary and sufficient conditions for the horizon formation in terms of inequalities relating a geometric quantity and a mass defined in an appropriate manner. In the case of infinitely thin spheroid, our results suggest a possibility of naked singularity formation by the spindle gravitational collapse in five-dimensional space-time.