Abelian Higgs Hair for Rotating and Charged Black Holes

TL;DR

This paper demonstrates that rotating and charged black holes can support vortex solutions of the Abelian Higgs field as hair, even in extremal cases, affecting the black hole geometry by inducing a deficit angle.

Contribution

It provides numerical evidence that Abelian Higgs vortex solutions can exist as hair around various black holes, including extremal ones, in both flat and AdS spacetimes, and analyzes their gravitational effects.

Findings

Black holes support Abelian Higgs vortex solutions as hair.

Vortex solutions exist even in extremal black holes without flux expulsion.

Vortices induce a deficit angle in the black hole spacetime.

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.