Green's-function analysis of the odd-parity perturbations of a Reissner-Nordström black hole

A Green's-function analysis is carried out for Reissner-Nordstr\"om odd-parity perturbation equations with sources. It leads to a definitive identification of the normal modes, which are shown to contain a derivative coupling of the gravitational and electromagnetic potentials to the background electromagnetic field. Connections are made with previous works by Gerlach in the high-frequency limit and by Chitre, Price, and Sandberg in the small-charge approximation.