No-bomb theorem for weakly magnetized Reissner-Nordström black holes: A linear-order analysis

We study the superradiant stability of magnetized Reissner–Nordström black holes against charged, massive scalar perturbations at linear order in the magnetization parameter b . At this order the Klein–Gordon equation is separable and the horizon acquires a magnetically induced angular velocity Ω H = 4 b Q / r + , enlarging the superradiant band to ω < m Ω H + q Φ H . Despite this enhancement, a sign analysis of the quartic governing the extrema of the effective potential–validated by numerical scans–shows that no exterior barrier–well forms, including in the eikonal scaling ( m , ℓ → ∞ with m b = O ( 1 ) ). Without a trapping well, quasi-bound superradiant modes do not arise, and the black-hole bomb is therefore absent. We conclude that Hod’s no-bomb theorem remains robust for weakly magnetized, non-rotating black holes at O ( b ) .