High overtone quasinormal modes of analog black holes and the small scale structure of the background fluid

Abstract

The goal of this paper is to build a foundation for, and explore the possibility of, using high overtone quasinormal modes (QNMs) 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 (BECs). In order to build this foundation, we first look into the hydrodynamic case where we calculate the high overtone QNM 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 QNMs of acoustic black holes in a BEC using the linearized Gross–Pitaevskii equation. We point out that at the high overtone QNM limit, the only term that is important in the linearized Gross–Pitaevskii equation is the quantum potential term, which is a small scale effect.