Spherically symmetric static spacetimes in vacuum f(T) gravity

Abstract

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 ) .