Quasinormal modes of Kerr black holes and beyond

The characteristic vibrational modes of a black hole are known as “quasinormal modes”, and they describe the response of a black hole after a perturbation and its subsequent gravitational wave emission. In this project, we will analyze the quasinormal modes of black holes in general relativity  (GR) and beyond. In the case of GR, the perturbations of Kerr black holes are described by the Teukolsky equation. We will employ Leaver’s continued fraction method to solve the Teukolsky equation and obtain the quasinormal mode frequencies of Kerr black holes, reproducing important results in the literature. Then we will consider a modified Teukolsky equation that describes perturbations of rotating black holes in extensions of GR and we will generalize the continued fraction method to solve this modified equation. We will compute the corrections to the Kerr quasinormal mode frequencies due to beyond-GR physics and we will study their phenomenological consequences. If time permits, we will also analyze the case of near-extremal black holes, which requires different methods.