Abelian Higgs Hair for Black Holes

TL;DR

This paper demonstrates that black holes can support Abelian Higgs vortices, providing a form of 'hair' that extends beyond traditional no-hair theorems, with potential observable effects at infinity.

Contribution

It presents evidence for black hole solutions with Abelian Higgs vortex hair, combining numerical and perturbative methods to show these configurations are physically plausible.

Findings

Black holes can support Nielsen-Olesen vortex solutions.

The vortex 'hair' can be measured from infinity.

These solutions extend the no-hair paradigm.

Abstract

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 non-trivial 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".