Regularization of 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, and 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.