The time evolution of unstable monopoles

The time evolution of unstable SO(3) monopole and dyon classical field configurations is studied numerically. It is found that as time goes on, a vacuum region of a finite radius r ∼ t develops, and the monopole core becomes a spherical shell of almost fixed thickness moving out at the speed of light. The monopole and dyon far fields persist outside the shell, with no indication of the emission of the nonabelian radiation expected as a manifestation of the instability under small perturbations in the far field region. Even an initially-growing perturbation eventually stabilizes and is split into a part that moves out to spatial infinity and another that moves in, is reflected in the vicinity of the monopole center, and then moves out. The general behavior is very similar to that of certain Minkowski-space, spherically-symmetric classical solutions discovered a few years ago. The stability of those solutions is also studied.