Abstract
We present teleparallel 3D gravity and we extract circularly symmetric solutions, showing that they coincide with the BTZ and Deser-de-Sitter solutions of standard 3D gravity. However, extending into f(T) 3D gravity, that is considering arbitrary functions of the torsion scalar in the action, we obtain BTZ-like and Deser-de-Sitter-like solutions, corresponding to an effective cosmological constant, without any requirement of the sign of the initial cosmological constant. Finally, extending our analysis incorporating the electromagnetic sector, we show that Maxwell-f(T) gravity accepts deformed charged BTZ-like solutions. Interestingly enough, the deformation in this case brings qualitatively novel terms, contrary to the pure gravitational solutions where the deformation is expressed only through changes in the coefficients. We investigate the singularities and the horizons of the new solutions, and amongst others we show that the cosmic censorship can be violated. Such novel behaviors reveal the new features that the f(T) structure brings in 3D gravity.
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