Perturbations of a rotating black hole. III - Interaction of the hole with gravitational and electromagnetic radiation

Immersed in an external radiation field, a rotating black hole scatters radiation and may either absorb or amplify it. The process is described by the set of homogeneous solutions to the separable wave equation which was previously derived in this series. Here we describe analytic and numerical techniques for obtaining these homogeneous solutions and interpreting them physically. New technical results include an explicit local transformation between perturbation quantities of opposite spin weight, a "conserved energy" for gravitational perturbations which allows the evidence for stability. of the Kerr metric to be further tightened, and an extension of the analytic results of Starobinsky and Churilov in the limit a M. Numerical results are presented which verify that the maximum superradiant amplification for gravitational waves is 138 percent; for electromagnetic waves the maximum is 4.4 percent (and is attained in a regime not susceptible to analytic treatment). The superradiance falls sharply with decreasing rotation a of the hole, or increasing mode numbers 1 and m. Subject headings: black holes - gravitation - relativity - rotation