Smooth static solutions of the Einstein-Yang/Mills equation
Joel Smoller, Arthur G. Wasserman, Shing-Tung Yau, J. Bryce McLeod
Abstract
We consider the Einstein/Yang-Mills equations in 3+1 space time dimensions with (2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymptotically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime.
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