Plamen Fiziev, Denitsa Staicova
Although finding numerically the quasinormal modes of a nonrotating black
hole is a well-studied question, the physics of the problem is often hidden
behind complicated numerical procedures aimed at avoiding the direct solution
of the spectral system in this case. In this article, we use the exact
analytical solutions of the Regge-Wheeler equation and the Teukolsky radial
equation, written in terms of confluent Heun functions. In both cases, we
obtain the quasinormal modes numerically from spectral condition written in
terms of the Heun functions. The frequencies are compared with ones already
published by Andersson and other authors. A new method of studying the branch
cuts in the solutions is presented -- the epsilon-method. In particular, we
prove that the mode $n=8$ is not algebraically special and find its value with
more than 6 firm figures of precision for the first time. The stability of that
mode is explored using the $\epsilon$ method, and the results show that this
new method provides a natural way of studying the behavior of the modes around
the branch cut points.
View original:
http://arxiv.org/abs/1109.1532
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