NO-HAIR THEOREM FOR SPHERICAL MONOPOLES AND DYONS IN SU(2) EINSTEIN YANG-MILLS THEORY

It is shown that spherically symmetric Einstein Yang-Mills (EYM) equations do not admit essentially non-Abelian asymptotically flat static solutions, which have non-zero YM charge and are non-singular, either globally or outside the horizon. This proves, under the assumption of spherical symmetry, that there are no globally regular static EYM monopoles and dyons, and that all static EYM black holes with non-zero YM charge belong to the Reissner-Nordstrom family.