Quasinormal modes and Regge poles of the canonical acoustic hole

TL;DR

This paper computes the quasinormal modes and Regge poles of the canonical acoustic hole, a black hole analogue, using multiple methods including time-domain evolution, asymptotic expansion, and numerical integration, providing insights into their properties.

Contribution

It introduces a comprehensive approach combining time-domain, asymptotic, and numerical methods to analyze quasinormal modes and Regge poles of the canonical acoustic hole.

Findings

Calculated quasinormal mode frequencies for low multipolar modes.

Derived an asymptotic expansion for frequencies and Regge poles.

Validated results through comparison with existing WKB and numerical methods.

Abstract

We compute the quasinormal mode frequencies and Regge poles of the canonical acoustic hole (a black hole analogue), using three methods. First, we show how damped oscillations arise by evolving generic perturbations in the time domain using a simple finite-difference scheme. We use our results to estimate the fundamental QN frequencies of the low multipolar modes $l=1, 2, \ldots$. Next, we apply an asymptotic method to obtain an expansion for the frequency in inverse powers of $l+1/2$ for low overtones. We test the expansion by comparing against our time-domain results, and (existing) WKB results. The expansion method is then extended to locate the Regge poles. Finally, to check the expansion of Regge poles we compute the spectrum numerically by direct integration in the frequency domain. We give a geometric interpretation of our results and comment on experimental verification.