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Modified gravity in three dimensional metric-affine scenarios

We consider metric-affine scenarios where a modified gravitational action is sourced by electrovacuum fields in a three dimensional space-time. Such scenarios are supported by the physics of crystalline structures with microscopic defects and, in particular, those that can be effectively treated as bi-dimensional (like graphene). We first study the case of $f(R)$ theories, finding deviations near the center as compared to the solutions of General Relativity. We then consider Born-Infeld gravity, which has raised a lot of interest in the last few years regarding its applications in astrophysics and cosmology, and show that new features always arise at a finite distance from the center. Several properties of the resulting space-times, in particular in presence of a cosmological constant term, are discussed.