Deciphering the Instability of the Black Hole Ringdown Quasinormal Spectrum

TL;DR

This paper analyzes the instability of black hole ringdown quasinormal mode spectra, providing an analytical explanation for their sensitivity to disturbances and discussing the robustness of certain observables.

Contribution

It introduces a transfer matrix approach to explain the instability of quasinormal modes and clarifies why some ringdown features remain robust despite perturbations.

Findings

Instability of quasinormal mode spectrum explained analytically.

Prompt ringdown response and greybody factors are robust observables.

Transfer matrix approach offers new insights into black hole perturbations.

Abstract

The spectrum of the quasinormal modes of the gravitational waves emitted during the ringdown phase following the merger of two black holes is of primary importance in gravitational astronomy. However, the spectrum is extremely sensitive to small disturbances of the system, thus potentially jeopardizing the predictions of the gravitational wave observables. We offer an analytical and intuitive explanation of such an instability and its properties based on the transfer matrix approach of quantum mechanics. We also give a simple interpretation of the fact that the prompt ringdown response in the time domain and the black hole greybody factor receive parametrically small corrections, thus being robust observables.