Spherically symmetric static spacetimes in vacuum f(T) gravity

TL;DR

This paper investigates vacuum solutions in f(T) gravity, showing Schwarzschild solutions persist in certain ultraviolet regimes and identifying de Sitter or BTZ-like solutions in infrared-deformed models relevant to cosmology.

Contribution

It demonstrates the persistence of Schwarzschild solutions in ultraviolet-deformed f(T) gravity and finds new vacuum solutions in infrared-deformed models, linking them to cosmological phenomena.

Findings

Schwarzschild geometry remains a vacuum solution in certain f(T) theories.

Infrared-deformed f(T) gravities admit de Sitter or BTZ-like solutions.

Vacuum solutions depend on the scale and deformation type of 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).