Abelian Higgs Hair for a Static Charged Black String

TL;DR

This paper demonstrates that four-dimensional electrically charged black strings can support vortex solutions of the Abelian Higgs field, which act as hair and induce a deficit angle in the spacetime geometry.

Contribution

It provides numerical evidence of vortex solutions as hair for charged black strings and analyzes their gravitational effects, including in extremal cases.

Findings

Black strings support Abelian Higgs vortex solutions.

Vortices induce a deficit angle in the black string spacetime.

Solutions exist even for extremal black strings.

Abstract

We study the problem of vortex solutions in the background of an electrically charged black string. We show numerically that the Abelian Higgs field equations in the background of a four-dimensional black string have vortex solutions. These solutions which have axial symmetry, show that the black string can support the Abelian Higgs field as hair. This situation holds also in the case of the extremal black string. We also consider the self-gravity of the Abelian Higgs field and show that the effect of the vortex is to induce a deficit angle in the metric under consideration.