The necessity of non-Riemannian acoustic spacetime in the fluids with vorticity

TL;DR

This paper discusses the importance of non-Riemannian acoustic spacetime, specifically acoustic torsion, in fluids with vorticity, highlighting its necessity even in rotational perturbations and its distinction from Riemannian structures.

Contribution

It demonstrates that non-Riemannian acoustic spacetime structures are essential in fluids with vorticity, extending previous work on gauge invariant sound equations.

Findings

Non-Riemannian acoustic spacetime exists in fluids with vorticity.

Riemannian structures are insufficient for describing such fluids.

Acoustic torsion is relevant even in rotational perturbations.

Abstract

The necessity of a newly proposed (PRD 70 (2004) 64004) non-Riemannian acoustic spacetime structure called acoustic torsion of sound wave equation in fluids with vorticity are discussed. It is shown that this structure, although not always necessary is present in fluids with vorticity even when the perturbation is rotational. This can be done by solving the Bergliaffa et al (Physica D (2004)) gauge invariant equations for sound, superposed to a general background flow, needs to support a non-Riemannian acoustic geometry in effective spacetime. Bergliaffa et al have previously shown that a Riemannian structure cannot be associated to this gauge invariant general system.