Abelian Higgs hair for extreme black holes and selection rules for snapping strings

TL;DR

This paper investigates whether extreme black holes can support Abelian Higgs vortex hair, finding that such vortices are expelled in the extreme limit and cannot stably attach, impacting models of string-black hole interactions.

Contribution

It demonstrates that Abelian Higgs vortices are expelled from extreme black holes, providing new insights into black hole hair and string interactions in extreme conditions.

Findings

Vortices are expelled from extreme black holes.

It is energetically unfavorable for vortices to interact with large extreme black holes.

Supports the idea that extreme black holes cannot support long Abelian Higgs hair.

Abstract

It has been argued that a black hole horizon can support the long range fields of a Nielsen-Olesen string, and that one can think of such a vortex as black hole ``hair''. We show that the fields inside the vortex are completely expelled from a charged black hole in the extreme limit (but not in the near extreme limit). This would seem to imply that a vortex cannot be attached to an extreme black hole. Furthermore, we provide evidence that it is energetically unfavourable for a thin vortex to interact with a large extreme black hole. This dispels the notion that a black hole can support `long' Abelian Higgs hair in the extreme limit. We discuss the implications for strings that end at black holes, as in processes where a string snaps by nucleating black holes.