Wave equations are derived in the Newman-Penrose formalism for gravitational and electromagnetic perturbations produced by charged and uncharged matter moving in a Reissner-Nordstr\"om background geometry. A brief sketch is given to obtain similar sets of equations in the Kerr-Newman background. The wave equations in the Kerr-Newman background, however, do not seem to separate, at least for the variables and the coordinate system used here.
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D. M. Chitre (1976) studied this question.
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