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 non-trivial 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.