SU(2) Yang-Mills solitons in AdS₄ spacetime

Abstract

We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2) theory. They are static, axially symmetric and approach at infinity the anti-de Sitter spacetime background. These configurations are characterized by a pair of integers (m, n), where m is related to the polar angle and n to the azimuthal angle, being related to the known flat space monopole-antimonopole chains and vortex rings. Generically, they describe composite configurations with several individual components, possesing a nonzero magnetic charge, even in the absence of a Higgs field. Such Yang-Mills configurations exist already in the probe limit, the AdS geometry supplying the attractive force needed to balance the repulsive force of Yang-Mills gauge interactions. The gravitating solutions are constructed by numerically solving the elliptic Einstein-DeTurck-Yang-Mills equations. The variation of the gravitational coupling constant α reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of α. The lower energy branch connects to the solutions in the global AdS spacetime, while the upper branch is linked to the generalized Bartnik-McKinnon solutions in asymptotically flat spacetime.

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

“…A different family of static BHs, in the Einstein-Maxwell-AdS system, was reported in[50] (see also[9,51]). work in this paper is also supported by the CIDMA strategic project UID/MAT/04106/2013 and by the EU grants NRHEP-295189-FP7-PEOPLE-2011-IRSES and H2020-MSCA-RISE-2015 Grant No.…”

Globally regular solutions to dyonic anti-de Sitter $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory -- Existence and characterising charges

“…and where {ρ k , σ k } are the constants defining the boundary conditions ar r = 0 (34). The appearance of hypergeometric functions in the regime |Λ| → ∞ is something which is familiar from globally regular solutions in the su(N ) case [13,22,37]; but for su(∞) solutions, we get the added 'bonus' that we can also calculate the gauge fields explicitly to all orders in , which is a satisfying result.…”

“…where ρ 1 = ρ1 (0) and σ 2 = σ2 (0) are constants which appear in (34). The functions xρ 1 (x) and x 2 σ2 (x) govern the spatial behaviour, and these are plotted (letting ρ 1 = σ 2 = 1) in Figures 1 and 2.…”

“…As well as black holes, much recent research has concerned solitons, which are purely magnetic, or dyons if they also involve the electric sector [8,13,31,[33][34][35][36][37]. These are a less famous but nevertheless interesting class of objects which began their life as Bartnik and McKinnon's 'particle-like solutions' to purely magnetic, asymptotically flat su(2) EYM field equations [38].…”