Formation of Five-Dimensional String Solutions from the Gravitational Collapse

TL;DR

This paper investigates how five-dimensional string solutions such as black strings and KK bubbles form from gravitational collapse, finding that black strings form reliably while KK bubbles do not, and naked singularities may develop.

Contribution

It demonstrates that collapsing matter in five dimensions always forms Gregory-Laflamme black strings, but not Kaluza-Klein bubbles, providing new insights into higher-dimensional gravitational collapse.

Findings

Black strings always form from collapse.

Kaluza-Klein bubbles do not form from collapse.

Naked singularities may develop in certain collapse scenarios.

Abstract

We study the formation of five-dimensional string solutions including the Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble, and the geometry with a naked singularity from the gravitational collapse. The interior solutions of five-dimensional Einstein equations describe collapsing non-isotropic matter clouds. It is shown that the matter cloud always forms the GL black string solution while the KK bubble solution cannot be formed. The numerical study seems to suggest that the collapsing matter forms the geometries with timelike naked curvature singularities, which should be taken cautiously as the general relativity is not reliable in the strong curvature regime.