Quasinormal modes of Kerr black holes using a spectral decomposition of the metric perturbations

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 ${10}^{-6}$ or better for $a\mathrm{/}M<0.8$, while it stays below $0.1\mathrm{\%}$ for $a\mathrm{/}M<0.98$.