Analogue of the pole-skipping phenomenon in acoustic black holes

TL;DR

This paper explores an analog of the pole-skipping phenomenon in acoustic black holes, linking it to quasinormal modes and dissipation, with potential experimental implications.

Contribution

It introduces the concept of pole-skipping in acoustic black holes and connects it to quasinormal modes and dissipation, extending black hole physics to laboratory analogs.

Findings

Pole-skipping points occur at negative imaginary Matsubara frequencies.

These points relate to the imaginary parts of quasinormal modes.

The phenomenon is connected to dissipation and instability timescales.

Abstract

The pole-skipping phenomenon is a special property of the retarded Green's function of black hole perturbations. We turn to its analog in acoustic black holes, which may relate to experiments. The frequencies of these special points are located at negative integer (imaginary) Matsubara frequencies $\omega=-i2\pi Tn$, which are consistent with the imaginary frequencies of quasinormal modes (QNMs). This implies that the lower-half plane pole-skipping phenomena have the same physical meaning as the imaginary part of QNMs, which represents the dissipation of perturbation of acoustic black holes and is related to the instability time scale of perturbation.