Analytic approach to the formation of a three-dimensional black string from a dust cloud

Abstract

In three-dimensional low-energy string theory,we study the formation of a black string from a dust cloud.We analytically obtain two distinct classes of exact solutions with arbitrary functionsresponsible for mass distributions ofthe dust cloud. The first and second kinds of solutions may describe collapsing dusts butthe first kind is only for inhomogeneous dust distribution while the second kind has a homogeneous limit.The finite collapse time and the Israel junction conditions tell us thatthe first kind solution describesa desired collapsing phenomenon, whereasthe scale factor in the inner spacetime for the second kindturns out to be trivial.In the first kind solution, specific collapsing models can be realized by choosing anappropriate inhomogeneousdust distribution consistent with the Israel junction conditions.Consequently, the inhomogeneous dust cloud eventually collapses to theblack string although the homogeneous dust clouddoes not guarantee the formation of the black string in our setting.The space-like curvature singularities occur at the finite collapse time andthey can be cloaked by the horizon of the black string.