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In this work we analyze the existence of electrically charged scalar cloudswhich are bound states of a complex-valued massive scalar field in thebackground of subextremal and extremal Kerr-Newman black holes (BH). Inparticular, we reanalyze neutral (uncharged) clouds in extremal Kerr BH's. Forthe extremal scenarios we have implemented a novel technique which allows us toobtain regular clouds at the BH horizon ${\cal H}^+$ which turn out to beconnected ``continuously'' with the cloud solutions in the subextremal caseeven if some derivatives of the scalar field are unbounded at the horizon. Inparticular, for subextremal BH's we have established regularity conditions at${\cal H}^+$, by demanding that the field and its radial derivatives arebounded there, but in the extremal scenarios we relax this last condition whiledemanding that some scalar invariants are well behaved at ${\cal H}^+$.Furthermore we have implemented an integral technique to understand and justifyin a simple and heuristic way the existence of such cloud configurations inthose BH backgrounds.

Regular scalar clouds around a Kerr-Newman black hole: subextremal and extremal scenarios