Spherically symmetric Yang-Mills solutions in a (4+n)-dimensional space-time

We consider the Einstein-Yang-Mills Lagrangian in a (4+n)-dimensional space-time. 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. If we assume the metric to be diagonal, we find that either n-1 of the gauge potentials associated with the n extra dimensions must vanish or the solutions are embedded abelian solutions. These latter are the Einstein-Maxwell-dilaton solutions in (4+n) dimensions. We present generic solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, which possesses n Higgs triplets coupled in a specific way to n independent dilaton fields. These solutions are the abelian Einstein-Maxwell- dilaton solutions and analytic nonabelian solutions, which have diverging Higgs fields. In addition, we construct numerically asymptotically flat and finite energy solutions for n=2. If we choose the metric to have off-diagonal components, generic solutions of the full model are possible. We present the numerical solutions for the case n=2.