New regular solutions with axial symmetry in Einstein–Yang–Mills theory

We construct new regular solutions in Einstein–Yang–Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by a pair of integers (k, n), where k is related to the polar angle and n to the azimuthal angle. The known spherically and axially symmetric EYM solutions have k = 1. For k > 1 new solutions arise, which form two branches. They exist above a minimal value of n, that increases with k. The solutions on the lower mass branch are related to certain solutions of Einstein–Yang–Mills–Higgs theory, where the nodes of the Higgs field form rings.  2005 Elsevier B.V. All rights reserved. 1. Introduction The well-known regular Bartnik–McKinnon (BM) solutions [1] and the corresponding non-Abelian black hole solutions [2], are asymptotically flat, static spherically symmetric solutions of SU(2) Einstein–Yang– Mills (EYM) theory. They are unstable solutions, sphalerons [3], and are characterized by the number of nodes of the gauge field. Besides the BM solutions there are also asymptotically flat, static, only axially symmetric regular and black hole solutions [4]. These E-mail address: kleihaus@marvin.physik.uni-oldenburg.de (B.