Gravitational field of a hedgehog and the evolution of vacuum bubbles

The gravitational field produced by a spherically symmetric "hedgehog" configuration in scalar field theories with global SO(3) symmetry (or higher) is studied in the limit in which these models become nonlinear models. The same gravitational effect can be generated by a set of cosmic strings intersecting at a point, in the limit that one considers a continuous distribution of such intersecting strings in a spherically symmetric configuration (to be referred to as the "string hedgehog"). When the energy densities associated with the hedgehog are small, we obtain a static geometry, but for higher values, the resulting geometry is that of an anisotropic cosmology. The evolution of bubbles joining two phases, one of which contains a hedgehog (as defined above) is investigated. The role of such configurations in processes that lead to classical false-vacuum destabilization and in the evolution of inflationary bubbles is discussed. The generalization of our results to the gauged case, i.e., to magnetic-monopole hedgehogs, is discussed.