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Smooth static solutions of the Einstein/Yang-Mills equations

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Abstract

We consider the Einstein/Yang-Mills equations in 3+1 space time dimensions withSU(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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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 48109-1003, Ann Arbor, MI, USA

    Joel A. Smoller & Arthur G. Wasserman

  2. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    S. -T. Yau

  3. Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA

    J. B. McLeod

Authors
  1. Joel A. Smoller
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  2. Arthur G. Wasserman
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  3. S. -T. Yau
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  4. J. B. McLeod
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Additional information

Communicated by A. Jaffe

Research supported in part by the NSF, Contract No. DMS 89-05205

Research supported in part by the ONR, Contract No. DOD-C-N-00014-88-K-0082

Research supported in part by the DOE, Grant No. DE-FG02-88ER25065

Research supported in part by the U.K. Science and Engineering Research Council

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Smoller, J.A., Wasserman, A.G., Yau, S.T. et al. Smooth static solutions of the Einstein/Yang-Mills equations. Commun.Math. Phys. 143, 115–147 (1991). https://doi.org/10.1007/BF02100288

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  • DOI: https://doi.org/10.1007/BF02100288

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