Abstract: Black hole (BH) perturbation theory is crucial in studying gravitational waves (GWs) emitted during the ringdown phase of binary BH mergers, or the quasinormal modes (QNMs). These QNMs carry essential information about the geometry around BHs and any potential deviations from General Relativity (GR). In recent years, there have been extensive studies of perturbations of BHs in modified gravity, but only for non-rotating or slowly rotating BHs. In this talk, I will present a new approach developed in arXiv:2206.10652 to study perturbations of BHs with arbitrary spin in modified gravity. This approach builds on Teukolsky’s foundational work in the 1970s for initially studying QNMs of rotating BHs in GR. I will first discuss how to derive the modified Teukolsky equation for BHs deforming not largely from their counterparts in GR to the leading and higher order in perturbation. To evaluate this equation, I will demonstrate how to implement all the necessary techniques, such as metric reconstruction. In the latter half of my talk, I will discuss applying this modified Teukolsky formalism to certain physical scenarios. Specifically, I will prescribe utilizing this formalism to study parity breaking in QNMs in certain modified gravity theories, such as dynamical Chern-Simons (dCS) gravity. I will also compare how QNMs are computed in dCS and higher derivative gravity, using either the traditional metric perturbation approach or this new approach.
