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The physical and mathematical properties of nonequatorial (m) scalar clouds that are supported by extremal Kerr black holes are studied analytically in the dimensionless large-mass M1 regime (here M is the mass of the central supporting black hole and, l, m are respectively the proper mass, the spheroidal harmonic index, and the azimuthal harmonic index of the linearized scalar field). In particular, we determine the discrete resonant spectrum m/l=m/l (M) that characterizes the composed black hole nonequatorial-scalar-field cloudy configurations. Interestingly, we reveal the existence of a critical dimensionless angular ratio, (m/l) ₌₀ₗ= (1+145) ^-1<1, above which maximally spinning Kerr black holes cannot support spatially regular bound-state configurations of the stationary massive scalar fields.
Shahar Hod (Wed,) studied this question.
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