Spherically symmetric static spacetimes in vacuum $f(T)$ gravity

We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional $f(T)$ gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed $f(T)$ gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Bañados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function $f(T)$.