Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions

Abstract

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1, with n>1. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particle-like solutions and black holes are constructed numerically for several values of D. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought as non-linear superpositions of Reissner-Nordstrom and non-Abelian configurations. A systematic discussion of the solutions is given for D=5, in which case the Reissner-Nordstrom black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact D=5 solution describing extremal black holes and solitons is also provided.

34 pages, 14 figures; v2: misprints corrected and references added

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• A non-Abelian Chern-Simons--Yang-Mills-Higgs system in 3+1 dimensions
• Static spherically symmetric black hole's solution in Einstein-Maxwell-Yang-Mills-dilaton theory
• Instantonic dyons of Yang-Mills--Chern-Simons models in d=2n+1 dimensions, n>2
• An instability of the Reissner-Nordstrom solution and new hairy black holes in d=5 dimensions
• Reissner-Nordström black holes with non-Abelian hair
• Non-Abelian clouds around Reissner-Nordström black holes: the existence line
• Charged isotropic non-Abelian dyonic black branes