Nonequatorial scalar clouds supported by maximally spinning Kerr black holes

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.