Schwarzschild solution in extended teleparallel 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.