Analogue of the pole-skipping phenomenon in acoustic black holes

Haiming Yuan,Xian-Hui Ge

doi:10.1140/epjc/s10052-022-10129-y

Haiming Yuan, Xian-Hui Ge

Open Access

https://doi.org/10.1140/epjc/s10052-022-10129-y

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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 =-i2pi 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.

Highlights

The retarded Green’s function is not unique at a special point in complex momentum space (ω, k) and this phenomenon is known as “pole-skipping” [1–3]
We have shown the consistency between pole-skipping points and quasinormal modes (QNMs) for Unruh’s acoustic black hole
We further conjecture that QNMs are consistent with the pole-skipping phenomenon in all cases of acoustic black holes

Summary

Introduction

The retarded Green’s function is not unique at a special point in complex momentum space (ω, k) and this phenomenon is known as “pole-skipping” [1–3]. We study the pole-skipping phenomenon in analogue black holes under various conditions The frequencies of these special points are located at negative integer (imaginary) Matsubara frequencies, similar to what was obtained in [4–7]. This, in turn, implies that the lower-half plane poleskipping points are related to the damping of black hole QNMs. we will consider the acoustic metric in curved spacetime. We consider that (2 + 1)-dimensional acoustic black hole metric embedded in Schwarzschild spacetime obtained from general relativistic fluids. We consider a (2 + 1)-dimensional acoustic black hole metric embedded in AdS-Schwarzschild spacetime obtained from the Gross–Pitaevskii equation . These locations are the poles of Green’s function that correspond to the hydrodynamic dispersion relation for momentum diffusion. Where rh,0 is the acoustic and event horizon, respectively

Discussion and conclusion

Acoustic black holes in Minkowski spacetime