On a transformation of Teukolsky’s equation and the electromagnetic perturbations of the Kerr black hole

Teukolsky’s equation, governing the perturbations (scalar, electromagnetic, and gravitational) of the Kerr black hole, is transformed, by a simple change of variables, in a manner such that there is formally no dif­ference in the treatments of the axisymmetric and the non-axisymmetric modes: the rôle of ‘m’ is effectively eliminated. By considering in detail the case of electromagnetic perturbations we show how, in all cases, the problems can be reduced to problems in the theory of penetration of one dimensional potential barriers with, however, certain novel features. The phenomenon of super-radiance, peculiar to the Kerr metric, emerges, for example, in an unexpected guise. The case of scalar perturbations is con­sidered briefly in an appendix.