Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-03-23
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, no figures, LaTeX file, corrections in some formulas, new references added, amendments in the text, authors contribu
Scientific paper
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 equations 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 the two different equations for $|s|=1/2$ 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.
Borissov Roumen S.
Fiziev Plamen P.
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