Non-Riemannian geometry of vortex acoustics

TL;DR

This paper extends the acoustic metric concept to include Cartan torsion in non-Riemannian geometry, revealing new analogies with superfluid vortices and suggesting applications to superfluid neutron star models.

Contribution

It introduces a non-Riemannian geometric framework for vortex acoustics, linking torsion in gravity to superfluid vortex phenomena and proposing new models for neutron star vortices.

Findings

Acoustic line element can be conformally mapped to a stationary torsion loop.

Torsion vector relates to superfluid vortex number and vorticity.

Torsion loops do not favor superfluid vortex formation.

Abstract

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.