Regular solutions of the Einstein–Yang–Mills equations

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Abstract
It is shown rigorously that any static symmetric solution of the Einstein–Yang–Mills (YM) equations with SU(2) gauge group that is well behaved in the far field is one of three types: black hole, particlelike, or Riessner–Nordström-like (RN) solution. (In particular, any solution with finite ADM mass is well behaved in the far field.) Black-hole solutions are proven to be analytic at the event horizon and thus coincides with Bartnik–McKinnon (BM) black holes. Furthermore, the singularity in the metric at the event horizon can be transformed away by a Kruskal-like change of coordinates in which the YM field remains well behaved. Particlelike solutions are shown to satisfy the same initial conditions as the BM solutions at r=0. RN-like solutions will be considered elsewhere.