New Torsional Deformations of Locally AdS${}_3$ Space

Abstract

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 $({\beta }_i)$ 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" ${\beta }_i$. Some of these new solutions describe deformations of the BTZ black hole due to the presence of torsion. The latter acts as a geometric flux which, in some cases, removes the causal singularity.

arXiv comment24 pages, 5 figures

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Cited by in corpus (1)

• Self-gravitating solutions in Yang-Mills-Chern-Simons theory coupled to 3D massive gravity