Massive charged scalar field in a Reissner–Nordstrom black hole background: quasinormal ringing

We compute characteristic (quasinormal) frequencies corresponding to decay of a massive charged scalar field in a Reissner–Nordstrom black hole background. It proves that, contrary to the behavior at very late times, at the stage of quasinormal ringing the neutral perturbations will damp slower than the charged ones. In the limit of the extremal black hole the damping rate of charged and neutral perturbations coincides. Possible connection of this with the critical collapse in a massive scalar electrodynamics is discussed.