  The concept of acoustic metric introduced previously by Unruh (PRL-1981) is
extended to include Cartan torsion by analogy with the scalar wave equation in
Riemann-Cartan (RC) spacetime. This equation describes irrotational
perturbations in rotational non-relativistic 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 when we choose the
static torsion loop in teleparallel gravity. In this case Cartan torsion vector
in the far from the vortex approximation is shown to be proportional to the
quantum vortex number of the superfluid. Also in this case the torsion vector
is shown to be proportional to the superfluid vorticity in the presence of
vortices. Torsion loops in RC spacetime does not favor the formation of
superfluid vortices. It is suggested that the teleparallel model may help to
find a model for superfluid neutron stars vortices based on non-Riemannian
gravity.
