A class of static spherically symmetric solutions in $f(T)$-gravity

We study a class of static spherically symmetric vacuum solutions in modified teleparallel gravity solving the field equations for a specific model Ansatz, requiring the torsion scalar $T$ to be constant. We discuss the models falling in this class. After some general considerations, we provide and investigate local solutions in the form of black holes and traversable wormholes as well as configurations that can match the anomalous rotation curves of galaxies.