The absence of static, smooth solutions in Einstein-Yang-Mills-Klein-Gordon theory

I study the existence of smooth, static nontrivial solutions to Einstein-Yang-Mills-Klein-Gordon equations. The absence of static solutions is proven if the Klein-Gordon field is linear and the asymptotic falloff of g00 to unity is quicker than 1/r. In the case when g00 = 1+0(1/r) the system is shown to reduce to the pure gravity, under certain conditions. Possible applications of bifurcation theory for finding solutions which are close to the trivial one in the case when the scalar field is of Higgs type are discussed. 12 refs. (author)