  Riemannian effective spacetime description of Hawking radiation in $^{3}He-A$
superfluids is extended to non-Riemannian effective spacetime. An example is
given of non-Riemannian effective geometry of the rotational motion of the
superfluid vacuum around the vortex where the effective spacetime Cartan
torsion can be associated to the Hawking giving rise to a physical
interpretation of effective torsion recently introduced in the literature in
the form of an acoustic torsion in superfluid $^{4}He$ (PRD-70(2004),064004).
Curvature and torsion singularities of this $^{3}He-A$ fermionic superfluid are
investigated. This Lense-Thirring effective metric, representing the superfluid
vacuum in rotational motion, is shown not support Hawking radiation when the
isotropic $^{4}He$ is restored at far distances from the vortex axis. Hawking
radiation can be expressed also in topological solitons (moving domain walls)
in fermionic superfluids in non-Riemannian (teleparallel) $(1+1)$ dimensional
effective spacetime. A teleparallel solution is proposed where the
quasiparticle speed is determined from the teleparallel geometry.
