Schwarzschild solution in extended teleparallel gravity

TL;DR

This paper derives an exact vacuum solution in extended teleparallel gravity using a specific tetrad field, revealing conditions under which the solution applies to linear $f(T)$ theories and analyzing its scalar torsion properties.

Contribution

The paper introduces a novel tetrad ansatz with an angle-dependent function and derives an exact vacuum solution in extended teleparallel gravity, expanding understanding of solutions in modified gravity theories.

Findings

Scalar torsion is constant in the derived solution.

Solution reduces to known cases when the angle function matches the polar angle.

Exact vacuum solution applicable to linear $f(T)$ gravity.

Abstract

Tetrad field, with two unknown functions of radial coordinate and an angle $\Phi$ which is the polar angle $\phi$ times a function of the redial coordinate, is applied to the field equation of modified theory of gravity. Exact vacuum solution is derived whose scalar torsion, $T ={T^\alpha}_{\mu \nu} {S_\alpha}^{\mu \nu}$, is constant. When the angle $\Phi$ coincides with the polar angle $\phi$, the derived solution will be a solution only for linear form of $f(T)$ gravitational theory.