The Einstein Yang-Mills equations: particle-like solutions for non-Abelian models

We investigate the particle-like solutions of the Einstein Yang-Mills equations for arbitrary gauge group. This requires a careful analysis of how the Lie algebraic structure of the Yang-Mills fields relates to the solutions of the differential equations. By introducing some new ideas, especially the use of invariant polynomials, we are able to solve previously intractable problems and gain new understanding in the context of non-Abelian models. In particular, we obtain the first numerical solutions for a non-Abelian model, construct a gauge-invariant reduction of the differential equations to the minimum number of variables, define a curvature, completely determine the possible asymptotic behaviour, and establish that previous suggestions for the non-existence of magnetically charged solutions have limited validity and that such solutions are entirely possible.