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

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

2004-03-31

arxiv.org/abs/hep-th/0403296v3

Class.Quant.Grav.22:183-194,2005

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0264-9381/22/1/012

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.

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