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arXiv · 2305.17168

New Torsional Deformations of Locally AdS$_3$ Space

Laura Andrianopoli·Bianca Letizia Cerchiai·Ruggero Noris·Lucrezia Ravera·Mario Trigiante·Jorge Zanelli
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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.

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Laura Andrianopoli, Bianca Letizia Cerchiai, Ruggero Noris, Lucrezia Ravera, Mario Trigiante, Jorge Zanelli. 2023-05-26. New Torsional Deformations of Locally AdS$_3$ Space. https://doi.org/10.1103/physrevd.108.044011

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