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 Mₙ 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/M<0. 8, while it stays below 0. 1% for a/M<0. 98.