Spherically symmetric solutions of a (4+n)-dimensional Einstein-Yang-Mills model with cosmological constant

Abstract

We construct solutions of an Einstein-Yang-Mills system including a cosmological constant in 4+n space-time dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric Ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge fields exist. We give the analytic solutions available in this model. These are ``embedded'' abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, where the higher dimensional cosmological constant induces a Liouville-type potential. The solutions are non-abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.

13 Tex-pages, 2 eps-figures; discussions changed; some points clarified

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• Higher order curvature generalisations of Bartnick-McKinnon and coloured black hole solutions in $d=5$
• Asymptotically non-flat rotating dilaton black holes
• Static solutions of a 6-dimensional Einstein-Yang-Mills model
• Spherically symmetric Yang-Mills solutions in a (4+n)- dimensional space-time
• Spherically symmetric Yang-Mills solutions in a 5-dimensional (Anti-) de Sitter space-time

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• Gravitating non-Abelian solitons and hairy black holes in higher dimensions
• Exact solutions of (n + 1)-dimensional Yang-Mills equations in curved space-time