Are gravitating magnetic monopoles stable?

The gravitating Julia-Zee dyon is a particle-like solution with both electric and magnetic charge. It is found in the Einstein-Yang-Mills-Higgs system of SU(2) with a scalar field in the adjoint representation coupled to gravity. Within the magnetic ansatz this system is reduced from describing dyons to describing the gravitating 't Hooft–Polyakov magnetic monopole. The stability of the well-known static gravitating magnetic monopole solutions with respect to perturbations within the magnetic ansatz-so-called magnetic perturbations-is well studied, but their stability with respect to perturbations outside the magnetic ansatz-so-called sphaleronic perturbations-is not. I undertake a purely numerical study by adding sphaleronic perturbations to gravitating magnetic monopole solutions and then dynamically evolving the system. For large perturbations I find that the system heads toward a dyon configuration, as expected. For sufficiently small perturbations, however, the system oscillates about the magnetic ansatz in a manner consistent with oscillations about a stable equilibrium.