Quasinormal ringing of Kerr black holes: The excitation factors

TL;DR

This paper calculates excitation factors for Kerr black hole perturbations, revealing how mode excitation varies with black hole spin and providing insights into gravitational wave signals during black hole ringdown.

Contribution

It introduces the first computation of excitation factors for general-spin Kerr black holes and analyzes their behavior in the extremal and large-damping limits.

Findings

Excitation factors tend to zero for corotating modes with l=m in the extremal limit.

Overtone contributions are more significant in fast-rotating black holes.

First analytical large-damping asymptotics for static black holes are presented.

Abstract

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A ``universal'', initial data-independent measure of the relative mode excitation is encoded in the poles of the Green's function that propagates small perturbations of the geometry (``excitation factors''). We compute for the first time the excitation factors for general-spin perturbations of Kerr black holes. We find that for corotating modes with $l=m$ the excitation factors tend to zero in the extremal limit, and that the contribution of the overtones should be more significant when the black hole is fast rotating. We also present the first analytical calculation of the large-damping asymptotics of the excitation factors for static black holes, including the Schwarzschild and Reissner-Nordstrom metrics. This is an important step to determine the convergence properties of the quasinormal mode expansion.