Classes of Exact Solutions to the Teukolsky Master Equation

TL;DR

This paper provides a unified framework for exact solutions to the Teukolsky Master Equation using confluent Heun functions, introducing new solutions and exploring their potential to model astrophysical jets.

Contribution

It offers a comprehensive classification of all exact solutions to the Teukolsky equations in terms of confluent Heun functions, including new solutions with potential astrophysical applications.

Findings

Found large classes of new exact solutions.

Identified polynomial solutions that describe collimated waves.

Demonstrated that linear combinations can model bounded astrophysical jets.

Abstract

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.