Superradiant Instability and Two Classes of Scalar Clouds around Kerr-Bertotti-Robinson Black Holes

Abstract: We investigate the dynamics of a charged massive scalar field around Kerr-Bertotti-Robinson Black Holes. By mapping the Klein-Gordon equation into a one-dimensional Schrödinger-like form and employing matched asymptotic expansions, we unveil the magnetic-field-induced quenching of the superradiant instability. We demonstrate that within a specific frequency band, the external magnetic field alters the physical boundary condition at the horizon from a propagating state to a purely exponentially decaying state, strictly locking the dissipation to zero ($\text{Im}(ω) = 0$). Consequently, the system supports two physically distinct classes of stationary bound states. Alongside the classical synchronized scalar clouds (Type-I) existing strictly at the superradiant threshold, we identify a new class of scalar clouds that exponentially decay at the event horizon (Type-II). Supported by precise numerical integrations, we demonstrate the spatial structure of these configurations. Our findings reveal that magnetized astrophysical environments can harbor significantly richer bosonic configurations than standard isolated black holes.