Resonances of a rotating black hole analogue

TL;DR

This paper investigates the resonant modes of a fluid flow analogue of a rotating black hole, using numerical simulations and geometric analysis to understand quasinormal modes, Regge poles, and their physical implications.

Contribution

It provides a comprehensive analysis of quasinormal and Regge pole resonances in a rotating black hole analogue, introducing a geodesic expansion and linking resonances to scattering phenomena.

Findings

Demonstrated the ubiquity of quasinormal ringing in the system.

Computed QN and RP spectra using numerical methods.

Linked Regge poles to scattering and absorption oscillations.

Abstract

Under certain conditions, sound waves in a fluid may be governed by a Klein-Gordon equation on an `effective spacetime' determined by the background flow properties. Here we consider the draining bathtub: a circulating, draining flow whose effective spacetime shares key features with the rotating black hole (Kerr) spacetime. We present a complete investigation of the role of quasinormal (QN) mode and Regge pole (RP) resonances of this system. First, we simulate a perturbation in the time domain by applying a finite-difference method, to demonstrate the ubiquity of `QN ringing'. Next, we solve the wave equation in the frequency domain with the continued-fraction method, to compute QN and RP spectra numerically. We then explore the geometric link between (prograde and retrograde) null geodesic orbits on the spacetime, and the properties of the QN/RP spectra. We develop a `geodesic expansion' method which leads to asymptotic expressions (in inverse powers of mode number $m$) for the spectra, the radial functions and the residues. Next, the role of the Regge poles in scattering and absorption processes is revealed through application of the complex angular momentum method. We elucidate the link between the Regge poles and oscillations in the absorption cross section. Finally, we show that Regge poles provide a neat explanation for `orbiting' oscillations seen in the scattering cross section.