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 BTZ-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).

8 pages. Some typos corrected and references updated. One additional typo corrected in Eq. (33). Accepted for publication in Physical Review D. Final version

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