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

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. Departamento de Fisica Teorica-Instituto de F́ısica , Universidade do Estado do Rio de Janeiro-UERJ, Rua São Francisco Xavier 524, Rio de Janeiro Brasil.Email:[email protected]