Quasibound states of Schwarzschild acoustic black holes

TL;DR

This paper investigates quasibound states and related phenomena in Schwarzschild acoustic black holes, providing spectral calculations and stability analysis, which could inform laboratory analog experiments of quantum gravity effects.

Contribution

It introduces a method to compute quasibound state spectra in Schwarzschild acoustic black holes using Heun functions, advancing understanding of their stability and resonant frequencies.

Findings

Calculated quasibound state frequencies and wave functions.

Analyzed stability of Schwarzschild acoustic black holes.

Compared resonant frequencies with standard Schwarzschild black holes.

Abstract

In this paper, we study the recently proposed Schwarzschild acoustic black hole spacetime, in which we investigate some physical phenomena related to the effective geometry of this background, including the analogous Hawking radiation and the quasibound states. We calculate the spectrum of quasibound state frequencies and the wave functions on the Schwarzschild acoustic background by using the polynomial condition of the general Heun function, and then we discuss the stability of the system. We also compare the resonant frequencies of the Schwarzschild acoustic black hole with the ones by the standard Schwarzschild black hole. Our results may shed some light on the physics of black holes and their analog models in condensed matter. Moreover, these studies could provide the possibility, in principle, for laboratory testing of effects whose nature is unquestionably associated with purely quantum effects in gravity.