Abstract: We present a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable. As an illustration of the method, we investigate massive vector (Proca) perturbations in the Kerr metric to second order in the spin parameter. We show that Proca fields exhibit a strong superradiant instability, with important astrophysical consequences.
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