New results for electromagnetic quasinormal and quasibound modes of Kerr black holes

Denitsa Staicova, Plamen Fiziev

Published 2014-12-12Version 1

The perturbations of Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of GR with astrophysics of compact objects, see the recent review article by Teukolsky [1]. The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equation and the Teukolsky Radial Equation, can be solved analytically in terms of confluent Heun functions. In this article, we use those exact solutions to obtain the electromagnetic (EM) quasinormal and quasibound spectra of the Kerr black hole. This is done by imposing the appropriate boundary conditions on the solutions and solving numerically the so obtained two-dimensional transcendental system. The EM quasinormal modes (QNM) spectra are found to match the already published results. Additionally, one obtains a symmetric with respect to the real axis spectrum corresponding to quasibound boundary conditions and also a spurious spectrum which can be shown to be numerically unstable. This new result demonstrates the importance of understanding the peculiarities of the numerical integration in understanding the physics of the problem. This may become particularly important considering the recent interest in the spectra of the electromagnetic counterparts of events producing gravitational waves.