A numerical study of the quasinormal mode excitation of Kerr black holes

TL;DR

This paper numerically investigates the excitation and properties of quasinormal modes in Kerr black holes, providing detailed comparisons with perturbation theory and insights into mode excitation and coupling.

Contribution

It introduces a systematic numerical method for extracting quasinormal mode frequencies and amplitudes in Kerr black holes, including overtones and mode coupling effects.

Findings

Excellent agreement between numerical and perturbation theory frequencies.

Amplitude of modes depends exponentially on the initial quasinormal regime start time.

Conditions for maximal excitation of mode pairs are identified.

Abstract

We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multi-block code which naturally allows for fixed adaptivity and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory. The amplitude of each mode depends exponentially on the starting time of the quasinormal regime, which is not defined unambiguously. We show that this time-shift problem can be circumvented by looking at appropriately chosen relative mode amplitudes. From our simulations we extract the quasinormal frequencies and the relative and absolute amplitudes of corotating and counterrotating modes (including overtones in the corotating case). We study the dependence of these amplitudes on the shape of the initial perturbation, the angular dependence of the mode and the black hole spin, comparing against results from perturbation theory in the so-called asymptotic approximation. We also compare the quasinormal frequencies from our numerical simulations with predictions from perturbation theory, finding excellent agreement. Finally we study under what conditions the relative amplitude between given pairs of modes gets maximally excited and present a quantitative analysis of rotational mode-mode coupling. The main conclusions and techniques of our analysis are quite general and, as such, should be of interest in the study of ringdown gravitational waves produced by astrophysical gravitational wave sources.