Resonant excitations of the 't Hooft-Polyakov monopole

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The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, Eₙ=ωₙ-iγₙ, satisfying the outgoing radiation condition. For n→∞, their frequencies ωₙ approach the mass of the vector boson, MW, while their lifetimes 1/γₙ tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breather-like excitation characterized by pulsations with a frequency approaching MW and with an amplitude decaying at late times as t⁻⁵/⁶.