Hairy rotating black string in the Einstein-Maxwell-Higgs system

TL;DR

This paper demonstrates numerically that rotating charged black strings can support Abelian Higgs field vortices, revealing new hair solutions and analyzing how rotation affects electric fields, vortex thickness, and spacetime geometry.

Contribution

It introduces vortex solutions as hair for rotating charged black strings and explores how rotation influences electric fields, vortex properties, and spacetime deficits.

Findings

Rotating black strings support Abelian Higgs vortex solutions.

Electric charge per unit length increases with rotation.

Vortex thickness decreases as rotation parameter increases.

Abstract

We show numerically that the Abelian Higgs field equations in the background of a four-dimensional rotating charged black string have vortex solutions. These solutions which have axial symmetry show that the rotating black string can support the Abelian Higgs field as hair. We find that one encounters with an electric field coupled to the Higgs scalar field for the case of rotating black string. This electric field is due to an electric charge per unit length, which increases as the rotation parameter becomes larger. We also find that the vortex thickness decreases as the rotation parameter grows up. Finally we 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 which decreases as the rotation parameter increases.