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

Abstract

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.

Black holes and gravitating axially symmetric non-abelian solitons in d = 3+1 and d = 4+1

“…Our solutions are akin to the static, axially symmetric EYM configurations in d = 4, studied exhaustively in [26], [27,28]. The regular and black hole solutions presented are natural generalisations of the known [10] d = 5 EYM spherically symmetric globally regular and black hole solutions.…”

“…As compared to the d = 4 case [27,28], we expect the existence of a much richer set of nonspherically symmetric EYM solutions in d = 5.…”

SU(2) Yang-Mills solitons in AdS4 spacetime

“…There a backbending in α is observed, with the occurrence of the second branch of solutions. With decreasing α, the solutions smoothly reach the corresponding (generalized) Bartnik-McKinnon solutions 8,25,52 in the limit α → 0. Along this branch, the mass of the (m, n) configurations is higher than the mass of the corresponding solution on the branch linked to the global AdS space.…”

“…Also, despite the generic presence of a net magnetic flux, they can be viewed as the natural AdS generalizations of the asymptotically flat EYM solitons in 24 . However, as discussed in 25 , the EYM system with Λ = 0 possesses a variety of other globally regular solutions, describing composite configurations, with several constituents b . In the notation of 25 , these solutions are characterized by a pair of positive integers (m, n), where m is related to the polar angle and n to the azimuthal angle.…”

Gravitating dyons with large electric charge

“…For monopole-antimonopole pair solutions and other composite solutions, in contrast, the second branch extends back to α = 0, where a pure Einstein-Yang-Mills solution is reached (after scaling w.r.t. α) [24,25,26,27].…”