Eluding the no-hair conjecture: Black holes in spontaneously broken gauge theories

TL;DR

This paper demonstrates the existence of non-trivial gauge and Higgs field configurations outside black holes in non-abelian gauge theories, challenging the traditional no-hair conjecture through numerical solutions.

Contribution

It shows that the no-hair theorem does not hold in non-abelian gauge theories and provides numerical evidence for black hole solutions with non-trivial fields in such theories.

Findings

Non-abelian black holes can have non-trivial external fields.

Numerical solutions for Einstein--Yang-Mills--Higgs system are obtained.

The study discusses stability considerations of these solutions.

Abstract

We study regular and black hole solutions to the coupled classical Einstein--Yang-Mills--Higgs system. It has long been thought that black hole solutions in the spontaneously broken phase of such a theory could have no nontrivial field structure outside of the horizon. We first show that the standard black hole no-hair theorem underlying this belief, although true in the abelian setting, does not necessarily extend to the non-abelian case. This indicates the possibility of solutions with non-trivial gauge and Higgs configurations decaying exponentially {\it outside} the horizon. We then find such solutions by numerical integration of the classical equations for the case of $SU(2)$ coupled to a Higgs doublet (the standard model less hypercharge). As a prelude to this work we also study regular and black hole solutions to Einstein--Non-Abelian--Proca theory and as a postscript we briefly discuss the important issue of stability.