Abelian Higgs hair for electrically charged dilaton black holes

Abstract

It is argued that an electrically charged dilaton black hole can support a long-range field of a Nielsen-Olesen string. Combining both numerical and perturbative techniques we examine the properties of an Abelian Higgs vortex in the presence of the black hole under consideration. Allowing the black hole to approach extremality we find that all fields of the vortex are expelled from the extreme black hole. In the thin string limit we obtain the metric of a conical electrically charged dilaton black hole. The effect of the vortex can be measured from infinity, justifying its characterization as black hole hair.