Quasinormal modes of Kerr black holes using a spectral decomposition of the metric perturbations
José Luis Blázquez-Salcedo, Fech Scen Khoo, Jutta Kunz, L. M. González-Romero
Abstract
We report a new method to calculate the quasinormal modes of rotating black holes, using a spectral decomposition to solve the partial differential equations that result from introducing linear metric perturbations to a rotating background. Our approach allows us to calculate a large sector of the quasinormal mode spectrum. In particular, we study the accuracy of the method for the ($l=2$)-led and ($l=3$)-led modes for different values of the ${M}_{z}$ azimuthal number, considering the fundamental modes as well as the first two excitations. We show that our method reproduces the Kerr fundamental modes with an accuracy of ${10}^{\ensuremath{-}6}$ or better for $a/M<0.8$, while it stays below 0.1% for $a/M<0.98$.