Abelian Higgs Hair for Electrically Charged Dilaton Black Holes

TL;DR

This paper investigates how an Abelian-Higgs vortex, representing a cosmic string, can exist as a long-range field around an electrically charged dilaton black hole, effectively acting as black hole hair.

Contribution

It demonstrates that Abelian-Higgs vortices can form stable long-range fields around charged dilaton black holes, and explores their properties near extremality and in the thin string limit.

Findings

Vortex fields are expelled from extremal black holes.

The metric of a conical charged dilaton black hole is derived.

Vortex effects are observable from infinity, confirming black hole hair.

Abstract

It is argued that an electronically 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 found that all fields of the vortex are expelled from the extreme black hole. In the thin string limit we obtained 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.