Abelian Higgs Hair for Rotating and Charged Black Holes

Abstract

We study the problem of vortex solutions in the background of rotating black holes in both asymptotically flat and asymptoticlly anti de Sitter spacetimes. We demonstrate the Abelian Higgs field equations in the background of four dimensional Kerr, Kerr-AdS and Reissner-Nordstrom-AdS black holes have vortex line solutions. These solutions, which have axial symmetry, are generalization of the Nielsen-Olesen string. By numerically solving the field equations in each case, we find that these black holes can support an Abelian Higgs field as hair. This situation holds even in the extremal case, and no flux-expulsion occurs. We also compute the effect of the self gravity of the Abelian Higgs field show that the the vortex induces a deficit angle in the corresponding black hole metrics.

arXiv comment22 pages, 16 figures, a section about the vortex self gravity on Kerr black hole added, extremal black holes considered, one figure changed, one reference added

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• Ringdown Spectroscopy of Rotating Black Holes Pierced by Cosmic Strings
• Exact \textit{pp}-waves, (A)dS waves and Kundt spaces in the Abelian-Higgs model
• Cosmological Black Holes on Branes
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