Wave equations are derived in the Newman-Penrose formalism for mixed electromagnetic and gravitational perturbations on both a flat spacetime background and a slightly charged (Q²GM²) Reissner-Nordstr\"om background. The physical meaning of these equations is discussed and analytical results are derived for nonrelativistic sources and for ultrarelativistic particle motions. The relationship between even-parity (TM) electromagnetic radiation multipoles in the long-wavelength approximation and static multipoles is shown to be the same as for classical radiation, suggesting a simple picture for electromagnetic radiation induced by gravitational perturbations.
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Chitre et al. (1975) studied this question.
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