Intertial Frame Dragging in an Acoustic Analogue spacetime

TL;DR

This paper explores the Lense-Thirring precession effect in an acoustic black hole analogue, deriving a formula for gyroscope precession near the ergosphere and discussing potential experimental detection.

Contribution

It introduces an exact formula for inertial frame dragging in acoustic black hole analogues and verifies it through geometric embedding, linking acoustic and gravitational precession effects.

Findings

Derived an exact precession frequency formula near the ergosphere.

Verified the formula through geometric embedding.

Discussed potential for experimental detection.

Abstract

We report an incipient exploration of the Lense-Thirring precession effect in a rotating \textit{acoustic analogue black hole} spacetime. An exact formula is deduced for the precession frequency of a gyroscope due to inertial frame dragging, close to the ergosphere of a `Draining Bathtub' acoustic spacetime which has been studied extensively for acoustic Hawking radiation of phonons and also for `superresonance'. The formula is verified by embedding the two dimensional spatial (acoustic) geometry into a three dimensional one where the similarity with standard Lense-Thirring precession results within a strong gravity framework is well known. Prospects of experimental detection of this new `fixed-metric' effect in acoustic geometries, are briefly discussed.