Spatially regular charged black holes supporting charged massive scalar clouds

Abstract

We prove that, as opposed to the familiar charged Reissner-Nordstr\"om black-hole spacetime, the spatially regular charged Ay\'on-Beato-Garc\'ia (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 $Q/M\ll1\ll M\mu$ of weakly charged black holes and large-mass fields, in which case it is proved that the dimensionless physical parameter $\alpha\equiv{{qQ}\over{M\mu}}$ must lie in the narrow interval $\alpha\in\big(\sqrt{{{3240}\over{6859}}},{{16}\over{23}}\big)$ [here $\{M,Q\}$ are the mass and electric charge of the central black hole and $\{\mu,q\}$ 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 $\{\alpha(M,Q,\mu,q;n\}^{n=\infty}_{n=0}$ of the composed charged-ABG-black-hole-charged-massive-scalar-field cloudy configurations can be determined {\it analytically} in the eikonal large-mass regime.