Static axially symmetric solutions of Einstein-Yang-Mills equations with a negative cosmological constant: The regular case

Numerical solutions of the Einstein-Yang-Mills equations with a negative cosmological constant are constructed. These axially symmetric solutions approach asymptotically the anti–de Sitter spacetime and are regular everywhere. They are characterized by the winding number $n>\mathrm{}1,$ the mass, and the non-Abelian magnetic charge. The main properties of the solutions and the differences with respect to the asymptotically flat case are discussed. The existence of axially symmetric monopole and dyon solutions in fixed anti–de Sitter spacetime is also discussed.