Electromagnetic Test Fields Around a Kerr-Metric Black Hole

Weak electromagnetic perturbations (test fields) in the exterior of a Kerr-metric black hole are studied. It is shown that (i) the only physically acceptable, time-independent perturbation is an axisymmetric field which corresponds to adding charge to the source and (ii) all axisymmetric normal modes are stable which, assuming completeness, guarantees stability for arbitrary axisymmetric perturbations. The proof of the nonexistence of time-independent, nonaxisymmetric test fields actually holds for perturbations associated with any physical (e.g., gravitational) field.