Long-lived resonances of massive scalar fields in the Reissner-Nordström black-hole spacetime: Analytic treatment in the large-mass regime

The physical and mathematical properties of the composed Reissner-Nordström-black-hole-massive-scalar-field system are studied {\it analytically} in the dimensionless large-mass $M\mu \gg 1$ regime [here $\{M,\mu \}$ are respectively the mass of the central black hole and the proper mass of the scalar field]. It is proved that, for a given value $\bar{Q}\equiv Q\mathrm{/}M$ of the dimensionless charge parameter of the central black hole, the system is characterized by the presence of quasi-resonances, linearized perturbation modes with arbitrarily long lifetimes. In particular, using analytical techniques, we determine the black-hole-field critical mass spectrum $\{M{\mu }_{\text{crit}}(\bar{Q})\}$ which characterizes the long-lived resonances of the composed physical system.