Non-Riemannian geometry of vortex acoustics

The concept of acoustic torsion is introduced by making use of the scalar wave equation in Riemann-Cartan spacetime. Acoustic torsion extends the acoustic metric previously given by Unruh (PRL-1981). The wave equation describes irrotational perturbations in rotational nonrelativistic fluids. This physical motivation allows us to show that the acoustic line element can be conformally mapped to the line element of a stationary torsion loop in non-Riemannian gravity. Two examples of such sonic analogues are given. The first is the stationary torsion loop in teleparallel gravity. In the far from the vortex approximation, the Cartan torsion vector is shown to be proportional to the quantum vortex number of the superfluid. The torsion vector is also shown to be proportional to the superfluid vorticity in the presence of vortices. The formation of superfluid vortices is shown not to be favored by torsion loops in Riemann-Cartan spacetime, as long as this model is concerned. It is suggested that the teleparallel model may help to find a model for superfluid neutron stars vortices based on non-Riemannian gravity.