Irrotational vortex geometry of torsion loops
  The irrotational vortex geometry carachter of torsion loops is displayed by showing that torsion loops and nonradial flow acoustic metrics are conformally equivalent in $(1+1)$ dimensions while radial flow acoustic spacetime are conformally related in $(2+1)$ dimensional spacetime. The analysis of 2-dimensional space allows us to express the fluid density in terms of the parameters of torsion loop metric. These results lead us to conclude that the acoustic metric of vortex flows is the gravitational analog of torsion loop spacetime. Since no vorticity in the fluids is considered we do not make explicit use of non-Riemannian geometry of vortex acoustics in classical fluids. Acoustic nonradial flows are shown to exihibit a full analogy with torsion loop metric. 
L.C. Garcia de Anddrade