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 σ 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.