Quasinormal ringing of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy

TL;DR

This paper analytically studies the excitation of quasinormal modes in Kerr black holes caused by particles falling radially with arbitrary energy, improving calculations of mode residues and coefficients, with applications in gravitational wave modeling.

Contribution

It extends previous methods to accurately compute quasinormal mode excitation factors and coefficients for Kerr black holes with particles falling along the axis, enhancing waveform predictions.

Findings

Higher overtones improve waveform agreement with numerical data.

Extended calculations of excitation factors for Kerr black holes.

Results aid in gravitational wave template development.

Abstract

The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green's function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode excitation for Kerr black holes. Relying on the formalism developed by Mano, Suzuki and Takasugi, we improve and extend previous calculations of the quasinormal mode residues in the complex frequency plane ("excitation factors" B_q). Using these results we compute the "excitation coefficients" C_q (essentially the mode amplitudes) in the special case where the source of the perturbations is a particle falling into the black hole along the symmetry axis. We compare this calculation with numerical integrations of the perturbation equations, and we show quantitatively how the addition of higher overtones improves the agreement with the numerical waveforms. Our results should find applications in models of the ringdown stage and in the construction of semianalytical template banks for gravitational-wave detectors, especially for binaries with large mass ratios and/or fast-spinning black holes.