Bulletin of the American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

Smooth static solutions of the Einstein-Yang/Mills equations

Author(s): J. Smoller; A. Wasserman; S. T. Yau; B. McLeod
Journal: Bull. Amer. Math. Soc. 27 (1992), 239-242.
MSC (2000): Primary 58E15; Secondary 53C80, 58G30, 81T13, 83C15
MathSciNet review: 1145579
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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.

References:

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[2]: R. Bartnik and J. McKinnon, Particlelike solutions of the Einstein-Yang Mills equations, Phys. Rev. Lett. 61 (1988), 141-144. MR 948143 (89e:83015)
[3]: S. Soleman, In New Phenomena in Subnuclear Physics (A. Zichichi, ed.), Plenum, New York 1975. MR 0436801 (55:9740)
[4]: S. Deser, Absence of static solutions in source-free Yang-Mills theory, Phys. Lett. B 64 (1976), 463-465.

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