Bulg. J. Phys. vol.37 no.2 (2010), pp. 065-089

Exact Solutions of Teukolsky Master Equation with Continuous Spectrum

R.S. Borissov, P.P. Fiziev
Physics Department, University of Sofia, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
Abstract. Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations on Kerr background satisfy Teukolsky Master Equation. The two non-trivial equations obtained after separating the variables are the polar angle equation and the radial equation. We solve them by transforming each one into the form of a confluent Heun equation. The transformation depends on a set of parameters, which can be chosen in a such a way, so the resulting angular and radial equations separately have simple polynomial solutions for neutrino, electromagnetic, and gravitational perturbations, provided some additional conditions are satisfied. Remarkably there exists a class of solutions for which these additional conditions are the same for both the angular and the radial equations for spins |s| = 1/2 and |s| = 1. As a result the additional conditions fix the dependence of the separation constant on the angular frequency but the frequency itself remains unconstrained and belongs to a continuous spectrum.

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