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Smooth static solutions of the Einstein-Yang/Mills equation

Joel Smoller·Arthur G. Wasserman·Shing-Tung Yau·J. Bryce McLeod
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Abstract

We consider the Einstein/Yang-Mills equations in $3+1$ space time dimensions with $\SU(2)$ 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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Joel Smoller, Arthur G. Wasserman, Shing-Tung Yau, J. Bryce McLeod. 1992-10-01. Smooth static solutions of the Einstein-Yang/Mills equation. https://doi.org/10.1007/bf02097002

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