Abelian Higgs hair for black holes

We find evidence for the existence of solutions of the Einstein and Abelian Higgs field equations describing a black hole pierced by a Nielsen-Olesen vortex. This situation falls outside the scope of the usual no-hair arguments due to the nontrivial topology of the vortex configuration and the special properties of its energy-momentum tensor. By a combination of numerical and perturbative techniques we conclude that the black hole horizon has no difficulty in supporting the long-range fields of the Nielsen-Olesen string. Moreover, the effect of the vortex can in principle be measured from infinity, thus justifying its characterization as black hole ‘‘hair.’’