Conversion of electromagnetic and gravitational waves by a charged black hole

In a strong electromagnetic field, gravitational waves are converted into electromagnetic waves of the same frequency, and vice versa. Here, we calculate scattering and conversion cross sections for a planar wave impinging upon a Reissner-Nordström black hole in electrovacuum, using the partial-wave expansion and numerical methods. We show that, at long wavelengths, the conversion cross section matches that computed by Feynman-diagram techniques, and at short wavelengths, the essential features are captured by a geometric-optics approximation. We demonstrate that the converted flux can exceed the scattered flux at large scattering angles, for highly-charged black holes. In the short-wavelength regime, the conversion effect may be understood in terms of a conversion phase that accumulates along a ray. We compute the scattering angle for which the converted and scattered fluxes are equal, as a function of charge-to-mass ratio; and we show that this scattering angle approaches 90° in the extremal limit.