Spatially regular charged black holes supporting charged massive scalar clouds
Shahar Hod
Abstract
We prove that, as opposed to the familiar charged Reissner-Nordstr\"om black-hole spacetime, the spatially regular charged Ay\'on-Beato-Garc\'{\i}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 $Q/M\ensuremath{\ll}1\ensuremath{\ll}M\ensuremath{\mu}$ of weakly charged black holes and large-mass fields, in which case it is proved that the dimensionless physical parameter $\ensuremath{\alpha}\ensuremath{\equiv}\frac{qQ}{M\ensuremath{\mu}}$ must lie in the narrow interval $\ensuremath{\alpha}\ensuremath{\in}(\sqrt{\frac{3240}{6859}},\frac{16}{23})$ [here ${M,Q}$ are the mass and electric charge of the central black hole and ${\ensuremath{\mu},q}$ 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 ${\ensuremath{\alpha}(M,Q,\ensuremath{\mu},q;n){}}_{n=0}^{n=\ensuremath{\infty}}$ of the composed charged-ABG-black-hole-charged-massive-scalar-field cloudy configurations can be determined analytically in the eikonal large-mass regime.