The canonical Bartnik-McKinnon solitons are regular solutions of the coupled Einstein-Yang-Mills system in which gravity may balance the repulsive nature of the Yang-Mills field. We examine the role played by gravity in balancing the system and determine its strength. In particular, we obtain an analytic lower bound on the fundamental mass-to-radius ratio, max(r) {2m (r)/r} > 2/3, which is a necessary condition for the existence of globally regular Einstein-Yang-Mills solitons. Our analytical results are in accord with numerical calculations. (c) 2007 Elsevier B.V. All rights reserved.
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