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, establish that the rotating black string can support the Abelian Higgs field as hair. We find an electric field coupled to the Higgs scalar field in the case of a rotating black string. This electric field is due to an electric charge-per-unit-length, which increases as the rotation parameter increases. We also find that the vortex thickness decreases as the rotation parameter increases. 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. PACS Nos.: 04.70.s, 04.40.b, 11.27.+d
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