High Overtone Quasinormal Modes of Analog Black Holes and the Small Scale Structure of the Background Fluid

TL;DR

This paper investigates high overtone quasinormal modes of analog black holes to explore their potential in probing the microscopic structure of the background fluid, with applications to quantum systems like Bose-Einstein condensates.

Contribution

It provides the first order correction to high overtone quasinormal mode frequencies for a 3+1D canonical non-rotating acoustic black hole and analyzes these modes in Bose-Einstein condensates.

Findings

First order correction to quasinormal mode frequencies obtained.

High overtone modes are dominated by the quantum potential term.

Potential use of quasinormal modes to study small scale quantum effects.

Abstract

The goal of this paper is to build a foundation for, and explore the possibility of, using high overtone quasinormal modes of analog black holes to probe the small scale (microscopic) structure of a background fluid in which an analog black hole is formed. This may provide a tool to study the small scale structure of some interesting quantum systems such as Bose-Einstein condensates. In order to build this foundation, we first look into the hydrodynamic case where we calculate the high overtone quasinormal mode frequencies of a 3+1 dimensional canonical non-rotating acoustic black hole. The leading order calculations have been done earlier in the literature. Here, we obtain the first order correction. We then analyze the high overtone quasinormal modes of acoustic black holes in a Bose-Einstein condensate using the linearized Gross-Pitaevskii equation. We point out that at the high overtone quasinormal mode limit, the only term that is important in the linearized Gross-Pitaevskii equation is the quantum potential term, which is a small scale effect.