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 (βi) and the singlet (τ) 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 AdS3 geometry is now deformed by effect of the "Beltrami-torsion"βi. Some of these new solutions describe deformations of the Bañados, 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.