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

Abstract

The necessity of a newly proposed [L.C. Garcia de Andrade, Phys. Rev. D 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 191 (2004) 121] 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.