Question of Abelian-Higgs hair expulsion from extremal dilaton black holes

Abstract

It has been argued that the extremal dilaton black holes exhibit a flux expulsion of Abelian-Higgs vortices. We carefully reexamine the problem and give analytic proofs for the flux expulsion to always take place. We also conduct a numerical analysis of the problem using three initial data sets on the horizon of an extreme dilatonic black hole, namely, core, vacuum, and sinusoidal initial conditions. We also show that an AbelianHiggs vortex can end on the extremal dilaton black hole. Concluding, we calculate the back reaction of the Abelian-Higgs vortex on the geometry of the extremal black hole and draw a conclusion that a straight cosmic string and the extreme dilatonic black hole hardly felt their presence.