Non-Riemannian vortex geometry of rotational viscous fluids and breaking of the acoustic Lorentz invariance

TL;DR

This paper extends the concept of acoustic torsion to rotational viscous fluids, demonstrating how viscosity and vorticity induce a non-Riemannian geometry that breaks Lorentz invariance, with implications for analog gravity models.

Contribution

It introduces a non-Riemannian vortex geometry for viscous fluids, generalizing the acoustic metric to include torsion and showing Lorentz invariance breaking due to viscosity and vorticity.

Findings

Acoustic torsion is extended to viscous fluids with vorticity.

Lorentz invariance is broken by acoustic torsion in the fluid.

An analog gravity model based on Lense-Thirring rotation is proposed.

Abstract

Acoustic torsion recently introduced in the literature (Garcia de Andrade,PRD(2004),7,64004) is extended to rotational incompressible viscous fluids represented by the generalised Navier-Stokes equation. The fluid background is compared with the Riemann-Cartan massless scalar wave equation, allowing for the generalization of Unruh acoustic metric in the form of acoustic torsion, expressed in terms of viscosity, velocity and vorticity of the fluid. In this work the background vorticity is nonvanishing but the perturbation of the flow is also rotational which avoids the problem of contamination of the irrotational perturbation by the background vorticity. The acoustic Lorentz invariance is shown to be broken due to the presence of acoustic torsion in strong analogy with the Riemann-Cartan gravitational case presented recently by Kostelecky (PRD 69,2004,105009). An example of analog gravity describing acoustic metric is given based on the teleparallel loop where the acoustic torsion is given by the Lense-Thirring rotation and the acoustic line element corresponds to the Lense-Thirring metric.