For generic f(T) gravity, all static cylindrical vacuum solutions take the same simple metric form with a constant torsion fixing an effective cosmological constant, and charged solutions follow a five-step construction.
The latter is brought to the following form once we eliminate T, Λ and G using (7), (34) and(39) r2F′ + (n − 4)rF + r2 F2 + 6 − 2n = 4r2V′2 fT(T(r)) A
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Cylindrically symmetric static $n$-dimensional (un)charged (anti-)de Sitter black holes in generic $f(T)$ gravity
For generic f(T) gravity, all static cylindrical vacuum solutions take the same simple metric form with a constant torsion fixing an effective cosmological constant, and charged solutions follow a five-step construction.