$D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity

Abstract: We present a $D$-dimensional charged Anti-de-Sitter black hole solutions in $f(T)$ gravity, where $f(T)=T+\beta T^2$ and $D \geq 4$. These solutions are characterized by flat or cylindrical horizons. The interesting feature of these solutions is the existence of inseparable electric monopole and quadrupole terms in the potential which share related momenta, in contrast with most of the known charged black hole solutions in General Relativity and its extensions. Furthermore, these solutions have curvature singularities which are milder than those of the known charged black hole solutions in General Relativity and Teleparallel Gravity. This feature can be shown by calculating some invariants of curvature and torsion tensors. Furthermore, we calculate the total energy of these black holes using the energy-momentum tensor. Finally, we show that these charged black hole solutions violate the first law of thermodynamics in agreement with previous results.