Classes of explicit special solutions to the scalar wave equation on black hole spacetime geometries are given. Some analogous solutions also exist for fields of spin one or two. The spin-zero radial equation on the Reissner-Nordström geometry with m = e and on the Kerr geometry with m = a is shown to be related to the Whittaker-Hill equation.
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W. E. Couch (1981) studied this question.
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