Non-Riemannian geometry of vortex acoustics

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.

Some additions to the last section: Demonstration that torsion vector is proportional to the number of vortices in the superfluid and some formulas omitted

References in corpus (5)

• On the dynamics of superfluid neutron star cores
• Wave Equation for Sound in Fluids with Vorticity
• Riemannian geometry of irrotational vortex acoustics
• Refringence, field theory, and normal modes
• Warped space-time for phonons moving in a perfect nonrelativistic fluid

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• Non-Riemannian acoustic spacetime of vortex hydrodynamics in Bose-Einstein condensates