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

TL;DR

This paper analytically investigates the formation of a three-dimensional black string from a dust cloud in string theory, identifying conditions under which collapse leads to black string formation.

Contribution

It provides exact solutions describing dust cloud collapse in 3D string theory, highlighting the role of inhomogeneity in black string formation.

Findings

Inhomogeneous dust clouds can collapse into black strings.

Homogeneous dust clouds do not necessarily form black strings.

Singularities are cloaked by the black string horizon.

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 functions responsible for mass distributions of the dust cloud. The first and second kinds of solutions may describe collapsing dusts but the 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 that the first kind solution describes a desired collapsing phenomenon, whereas the scale factor in the inner spacetime for the second kind turns out to be trivial. In the first kind solution, specific collapsing models can be realized by choosing an appropriate inhomogeneous dust distribution consistent with the Israel junction conditions. Consequently, the inhomogeneous dust cloud eventually collapses to the black string although the homogeneous dust cloud does not guarantee the formation of the black string in our setting. The space-like curvature singularities occur at the finite collapse time and they can be cloaked by the horizon of the black string.