Abstract
The covariant Klein–Gordon equation in the Kerr–Newman black hole geometry is separated into a radial part and an angular part. It is discovered that in the nonextreme case, these two equations belong to a generalized spin-weighted spheroidal wave equation. Then general exact solutions in integral forms and several special solutions with physical interest are given. While in the extreme case, the radial equation can be transformed into a generalized Whittaker–Hill equation. In both cases, five-term recurrence relations between coefficients in power series expansion of general solutions are presented. Finally, the connection between the radial equations in both cases is discussed.
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