Local Lorentz transformation and exact spherically symmetric vacuum solutions in f(T) gravity theories

TL;DR

This paper derives exact spherically symmetric vacuum solutions in f(T) gravity using a non-diagonal tetrad and analyzes their properties, revealing they correspond to Schwarzschild-Ads spacetime.

Contribution

It introduces a non-diagonal tetrad approach with an arbitrary function to find exact vacuum solutions in f(T) gravity, linking them to known Schwarzschild-Ads spacetime.

Findings

Solutions are analytically derived with integration constants.

The solutions correspond to Schwarzschild-Ads spacetime.

Conserved charges are calculated for each solution.

Abstract

Applying a non-diagonal spherically symmetric tetrad field having arbitrary function, $S(r)$, that is corresponding to local Lorentz transformation, to the field equations of f(T) gravity theories. An analytic vacuum solutions with constants of integration are derived. These constants are studied by calculating the total conserved charge associated to each solution. The study has shown that the obtained solutions represent Schwarzschild-Ads spacetime.