Superconducting Hair on Charged Black String Background

Behaviour of Dirac fermions in the background of a charged black string penetrated by an Abelian Higgs vortex is elaborated. One finds the evidence that the system under consideration can support fermion fields acting like a superconducting cosmic string in the sence that a nontrivial Dirac fermion field can be carried by the system in question. The case of nonextremal and extremal black string vortex systems were considered. The influence of electric and Higgs charge, the winding number and the fermion mass on the fermion localization near the black string event horizon was studied. It turned out that the extreme charged black string expelled fermion fields more violently comparing to the nonextremal one.