Abstract
We construct new family of spherically symmetric regular solutions of SU(2) Yang–Mills theory coupled to pure R2 gravity. The particle-like field configurations possess non-integer non-Abelian magnetic charge. A discussion of the main properties of the solutions and their differences from the usual Bartnik–McKinnon solitons in the asymptotically flat case is presented. It is shown that there is continuous family of linearly stable non-trivial solutions in which the gauge field has no nodes.
Highlights
Modified theories of gravity gained increasing interest in past decade since it seems accepted that the inflationary scenario in the early Universe is related with modification of the usual Einstein–Hilbert action [1], in particular via addition of the quadratic curvature terms
An interesting observation is that a variety of features of asymptotically flat self-gravitating BM solutions and the corresponding hairy black holes are not shared by their counterparts in the asymptotically anti-de Sitter (AdS) space–time [33,34,35,38]
We found that the R2 EYM model has only solutions with no node in the gauge field profile function, or with a single node, there is no solutions with multiple nodes
Summary
Modified theories of gravity gained increasing interest in past decade since it seems accepted that the inflationary scenario in the early Universe is related with modification of the usual Einstein–Hilbert action [1], in particular via addition of the quadratic curvature terms. Localized particle-like solutions of the classical Yang– Mills theory coupled to the usual gravity have been the subject of long standing research interest since Bartnik and McKinnon found these solutions in 1988 [15]. These globally regular self-gravitating field configurations were discovered numerically in the asymptotically flat SU(2) Einstein–Yang–Mills (EYM) theory. An interesting observation is that a variety of features of asymptotically flat self-gravitating BM solutions and the corresponding hairy black holes are not shared by their counterparts in the asymptotically anti-de Sitter (AdS) space–time [33,34,35,38]. The main purpose of this work is to explicitly construct R2 counterparts of the spherically symmetric solutions of the EYM system, looking for new features induced by the different structure of the gravitational part of the action
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