Horizon-evanescent scalar clouds from coupled rotation and magnetic fields around black holes

A bstract We show that black-hole rotation and an external magnetic field can jointly generate a distinct class of scalar clouds. Using the Kerr-Bertotti-Robinson geometry as a separable laboratory for magnetized rotating black holes, we study a charged massive scalar field and map the radial Klein-Gordon equation into a one-dimensional Schrödinger-like form. The magnetic coupling shifts the near-horizon dispersion relation and realizes a positive horizon gap: a sufficient near-horizon criterion under which the horizon wavenumber becomes purely imaginary in a finite frequency band below the usual kinematic synchronization frequency. In this band the physical horizon boundary condition is no longer a propagating ingoing wave, but a regular exponentially decaying state. This rotation-magnetic-field mechanism quenches the superradiant flux and supports horizon-decaying scalar clouds (Type-II), distinct from the usual synchronized propagating clouds (Type-I). Matched asymptotic expansions and numerical shooting solutions are used to exhibit both branches and their spatial profiles. Thus the Kerr-Bertotti-Robinson solution is not an isolated curiosity, but an explicit realization of a broader positive-gap criterion for horizon-evanescent stationary configurations that are absent in isolated Kerr systems.