New torsional deformations of locally AdS3 space

We consider general torsion components in three-dimensional Einstein-Cartan gravity, providing a geometrical interpretation for matter, and find new solutions of the corresponding equations for the Riemann curvature and torsion. These geometries involve a peculiar interplay between the vector (ss(i)) and the singlet (tau) irreducible components of the torsion which, under general conditions, feature a formal analogy with the equation for a Beltrami fluid. Interestingly, we find that the local AdS(3) geometry is now deformed by effect of the "Beltrami-torsion" ss(i). Some of these new solutions describe deformations of the Banados, Teitelboim, Zanelli black hole due to the presence of torsion. The latter acts as a geometric flux which, in some cases, removes the causal singularity.