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Smooth static solutions of the Einstein/Yang-Mills equations

Joel A Smoller Arthur G Wasserman Shing-Tung Yau JB McLeod

Mathematical Physics mathscidoc:1912.43495

Communications in mathematical physics, 143, (1), 115-147, 1991.12
We consider the Einstein/Yang-Mills equations in 3+1 space time dimensions with<i>SU</i>(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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@inproceedings{joel1991smooth,
  title={Smooth static solutions of the Einstein/Yang-Mills equations},
  author={Joel A Smoller, Arthur G Wasserman, Shing-Tung Yau, and JB McLeod},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203610408107059},
  booktitle={Communications in mathematical physics},
  volume={143},
  number={1},
  pages={115-147},
  year={1991},
}
Joel A Smoller, Arthur G Wasserman, Shing-Tung Yau, and JB McLeod. Smooth static solutions of the Einstein/Yang-Mills equations. 1991. Vol. 143. In Communications in mathematical physics. pp.115-147. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203610408107059.
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