Gravitational waveform model based on photon motion for spinning black holes

Abstract

The waveforms from binary black hole mergers include inspiral, merger and ringdown parts. Usually, the inspiral waveform can be obtained by calibrating from post-Newtonian approximation;The merger and ringdown ones can be gotten from the quasi-normal modes (QNMs) with black hole perturbation theory. However, for more general black holes, the calculation of the quasi-normal modes is not trivial. In this paper we use the photon sphere to get the quasi-normal modes of spinning black hole. Then we connect the ringdown wave with the inspiral part to get full waveforms and compare with the ones from numerical relativity(NR). We find that they match with each other very well. In principle this method can be extended to arbitrary black holes. As an example, the ringdown waveforms from parametrized axisymmetric black hole are obtained. We also use this method to get ringdown signals of the accelerating final black hole due to gravitational recoil during the merger. Even for the extreme cases, the acceleration due to the recoil can not produce detectable effects.