DYNAMICS OF EUCLIDEANIZED EINSTEIN-YANG-MILLS SYSTEMS WITH ARBITRARY GAUGE GROUPS

We describe the dynamics of euclideanized SO(4)-symmetric Einstein-Yang-Mills (EYM) systems with arbitrary compact gauge groups K. For the case of SO(n) and SU(n) gauge groups and simple embeddings of the isotropy group in K, we show that in the resulting dynamical system, the Friedmann equation decouples from the Yang-Mills equations. Furthermore, the latter can be reduced to a system of two second-order differential equations. This allows us to find a broad class of instanton (wormhole) solutions of the EYM equations. These solutions are not afflicted by the giant-wormhole catastrophe.