Formation of Three-Dimensional Black Strings from Gravitational Collapse of Dust Cloud

We study the formation of black strings from a gravitational collapse of cylindrical dust clouds in the three-dimensional low-energy string theory. A new junction condition for the dilaton as well as two junction conditions for metrics and extrinsic curvatures between both regions of the clouds is presented. As a consequence, it is found that the collapsing dust cloud always collapses to a black string within a finite collapse time, and then a curvature singularity formed at origin is cloaked by an event horizon. Moreover, it is also found that the collapse process can form a naked singularity within finite time, regardless of the choice of initial data.