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We study regular and black hole solutions to the coupled classicalEinstein--Yang-Mills--Higgs system. It has long been thought that black holesolutions in the spontaneously broken phase of such a theory could have nonontrivial field structure outside of the horizon. We first show that thestandard black hole no-hair theorem underlying this belief, although true inthe abelian setting, does not necessarily extend to the non-abelian case. Thisindicates the possibility of solutions with non-trivial gauge and Higgsconfigurations decaying exponentially {\it outside} the horizon. We then findsuch solutions by numerical integration of the classical equations for the caseof $SU(2)$ coupled to a Higgs doublet (the standard model less hypercharge).  As a prelude to this work we also study regular and black hole solutions toEinstein--Non-Abelian--Proca theory and as a postscript we briefly discuss theimportant issue of stability.Comment: 35 pages, phyzzx, (CLNS-92/1162, CTP-2160

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