Quasinormal modes and stability of the rotating acoustic black hole: numerical analysis

TL;DR

This paper numerically analyzes the quasinormal modes of a 2+1D rotating acoustic black hole, demonstrating its stability against small perturbations by examining frequency behavior as the rotation parameter varies.

Contribution

It provides the first full non-linear numerical analysis of quasinormal modes for the rotating draining bathtub acoustic black hole, a key analogue to Kerr black holes.

Findings

The real and imaginary parts of QNM frequencies are computed as a function of rotation.

The imaginary part of the frequency remains positive, indicating stability.

The acoustic black hole remains stable under small perturbations across the studied parameter range.

Abstract

The study of the quasinormal modes (QNMs) of the 2+1 dimensional rotating draining bathtub acoustic black hole, the closest analogue found so far to the Kerr black hole, is performed. Both the real and imaginary parts of the quasinormal (QN) frequencies as a function of the rotation parameter B are found through a full non-linear numerical analysis. Since there is no change in sign in the imaginary part of the frequency as B is increased we conclude that the 2+1 dimensional rotating draining bathtub acoustic black hole is stable against small perturbations.