Quasinormal modes and excitation factors of Kerr black holes

Abstract: Theoretical understanding of the characteristic oscillations of a perturbed black hole, also referred to as quasinormal modes (QNMs), is crucial to interpreting the late stage of binary black hole mergers that we now routinely observe in gravitational wave detectors. In this work, we introduce a new approach, based on the generalized Sasaki-Nakamura formalism, to compute the QNM spectra and their excitation factors (QNEFs), for scalar, electromagnetic and gravitational perturbations. Using this approach, QNM wavefunctions remain finite at the horizon and spatial infinity. Our results in general agree with previous calculations that were performed using different methods, though we further clarify that QNEFs and their scaling with the mass of the black hole depend on the spin-weight of the perturbation. We show that avoided crossing is not a general phenomenon: the real or the imaginary part of the eigenvalues can cross each other but not both simultaneously, and when crossing occurs in one part, repulsion follows in the another part. Eigenvalue repulsion, originating from branch point singularities, still plays an important role in the QNM spectra, despite the fact that the spectra depend only on the real-valued black hole angular momentum.