Spatially regular charged black holes supporting charged massive scalar clouds

We prove that, as opposed to the familiar charged Reissner-Nordstr\"om black-hole spacetime, the spatially regular charged Ay\'on-Beato-Garc\'{}a (ABG) black-hole spacetime can support charged scalar clouds, spatially regular stationary matter configurations which are made of linearized charged massive scalar fields. Interestingly, we reveal the fact that the composed black-hole-field system is amenable to an analytical treatment in the regime Q/M1Mμ of weakly charged black holes and large-mass fields, in which case it is proved that the dimensionless physical parameter α≡qQMμ must lie in the narrow interval α∈(√3240/6859,16/23) [here M,Q are the mass and electric charge of the central black hole and μ,q are the proper mass and charge coupling constant of the supported scalar field]. In particular, we explicitly prove that, for weakly charged black holes, the discrete resonance spectrum α(M,Q,μ,q;n)ₙ₌₀^n=∞ of the composed charged-ABG-black-hole-charged-massive-scalar-field cloudy configurations can be determined analytically in the eikonal large-mass regime.