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

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 nontrivial gauge and Higgs configurations decaying exponentially 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.