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

Abstract

The first nonexistence result in the sourceless Yang-Mills theory is due to Deser [1], who has shown that there are no nonzero static finite energy solutions. Then many authors [2, 3] proved nonexistence of time-dependent solitons in Yang-Mills theory. Glassey and Strauss [3] demonstrated the absence of static solitons and solitary waves in Yang-Mills- -Klein-Gordon theory. Recently Weder [4] proved the absence of nonsingular, localized solutions to Einstein-Yang-Mills equations. His result needed a strong falloff of g00 at infinity and therefore met a critique [5]. Deser [5] attacked the same problem in (2+1) space-time dimensions, to get the desired nonexistence result. Finally in [6] it was shown that the linear scalar (Schrödinger or Klein-Gordon) and nonlinear (under simple restrictions on the nonlinearities) field coupled to Yang-Mills fields has no static nonzero finite energy solutions[…]