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.
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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.