Classes of exact solutions to the Teukolsky master equation

The Teukolskymaster equation is the basic tool for the 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.