Stability of self-gravitating magnetic monopoles

The stability of a spherically symmetric self-gravitating magnetic monopole is examined in the thin wall approximation: modeling the interior false vacuum as a region of de Sitter space; the exterior as an asymptotically flat region of the Reissner-Nordström geometry; and the boundary separating the two as a charged domain wall. There remains only to determine how the wall gets embedded in these two geometries. In this approximation, the ratio k of the false vacuum to surface energy densities is a measure of the symmetry breaking scale η. Solutions are characterized by this ratio, the charge on the wall Q, and the value of the conserved total energy M. We find that for each fixed k and Q up to some critical value, there exists a unique globally static solution, with M≃Q^3/2; any stable radial excitation has M bounded above by Q, the value assumed in an extremal Reissner-Nordström geometry, and these are the only solutions with M<Q. As M is raised above Q a black hole forms in the exterior: (i) for low Q or k, the wall is crushed; (ii) for higher values, it oscillates inside the black hole. If the mass is not too high the former solutions coexist with an inflating bounce; (iii) for k, Q or M outside the above regimes, there is a unique inflating solution. In case (i) the course of the bounce lies within a single asymptotically flat region (AFR) and it resembles closely the bounce exhibited by a false vacuum bubble (with Q=0). In case (iii) the course of the bounce spans two consecutive AFRs. However, for an asymptotic observer it resembles a monotonic false vacuum bubble.