Regularization of f(T)f(T) gravity theories and local Lorentz transformation

We regularized the field equations of $f(T)$ gravity theories such that the effect of Local Lorentz Transformation (LLT), in the case of spherical symmetry, is removed. A "general tetrad field", with an arbitrary function of radial coordinate preserving spherical symmetry is provided. We split that tetrad field into two matrices; the first represents a LLT, which contains an arbitrary function, the second matrix represents a proper tetrad field which is a solution to the field equations of $f(T)$ gravitational theory, (which are not invariant under LLT). This "general tetrad field" is then applied to the regularized field equations of $f(T)$. We show that the effect of the arbitrary function which is involved in the LLT invariably disappears.Comment: 12 page

Schwarzschild solution in extended teleparallel gravity

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.Comment: 8 pages Late