Formation of five-dimensional string solutions from gravitational collapse

We study the formation of five-dimensional string solutions including the Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble and geometry with a naked singularity from 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 time-like naked curvature singularities, which should be taken cautiously as general relativity is not reliable in the strong curvature regime.