Quasinormal modes of nearly extremal Kerr spacetimes: Spectrum bifurcation and power-law ringdown

We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal-mode frequencies presented in a recent paper [H. Yang et al., Phys. Rev. D 87, 041502 (2013)]. One set of modes that we call zero-damping modes has vanishing imaginary part in the extremal limit and exists for all corotating perturbations (i.e. modes with azimuthal index m >= 0). The other set (the damped modes) retains a finite decay rate even for extremal Kerr black holes and exists only for a subset of corotating modes. As the angular momentum approaches its extremal value, the frequency spectrum bifurcates into these two distinct branches when both types of modes are present. We discuss the physical reason for the mode branching by developing and using a bound-state formulation for the perturbations of generic Kerr black holes. We also numerically explore the specific case of the fundamental l = 2 modes, which have the greatest astrophysical interest. Using the results of these investigations, we compute the quasinormal-mode response of a nearly extremal Kerr black hole to perturbations. We show that many superimposed overtones result in a slow power-law decay of the quasinormal ringing at early times, which later gives way to exponential decay. This exceptional early-time power-law decay implies that the ringdown phase is long lived for black holes with large angular momentum, which could provide a promising strong source for gravitational-wave detectors.