Classes of Exact Solutions to the Teukolsky Master Equation

Details Classes of Exact Solutions to the Teukolsky Master Equation Classes of Exact Solutions to the Teukolsky Master Equation

2009-08-28

arxiv.org/abs/0908.4234v4

Class. Quant. Grav.27:135001, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, LaTeX file, no figures. Final version

Scientific paper

10.1088/0264-9381/27/13/135001

The Teukolsky Master Equation is the basic tool for study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky Radial Equation and the Teukolsky Angular Equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confluent Heun functions. Large classes of new exact solutions are found and classified with respect to their characteristic properties. Special attention is paid to the polynomial solutions which are singular ones and introduce collimated one-way-running waves. It is shown that a proper linear combination of such solutions can present bounded one-way-running waves. This type of waves may be suitable as models of the observed astrophysical jets.

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