Analogue of the pole-skipping phenomenon in acoustic black holes

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.