Analytic properties of the solutions of Teukolsky's equation

A method is proposed for studying the low-frequency solutions of Teukolsky's equation, describing the behavior of massless fields in the vicinity of a Kerr black hole. Approximate basis solutions and an integral equation for exact solutions are constructed. The analytic properties of the exact solutions and the asymptotic behavior of the leading nonanalytic parts are investigated and the approximate solutions are estimated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 47–51, July, 1981.The author is grateful to Professor K. A. Piragas and the participants of the seminar directed by him for their attention to the present work and for useful discussions.