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

Energy of spherically symmetric spacetimes on regularizing teleparallelism

We calculate the total energy of an exact spherically symmetric solutions, i.e., Schwarzschild and Reissner Nordstr$\ddot{o}$m, using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical! Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.Comment: 13 pages, Latex, No Figure, Will appear in IJMP

Wormhole solution and Energy in Teleparallel Theory of Gravity

An exact solution is obtained in the tetrad theory of gravitation. This solution is characterized by two-parameters $k_1, k_2$ of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation $\rho=\rho_t=0$ with $\rho=T_{i,j}u^iu^j$, $\rho_t=(T_{ij}-\displaystyle{1 \over 2}Tg_{ij}) u^iu^j$ where $u^iu_i=-1$. From this solution which contains an arbitrary function we can generates the other two solutions obtained before. The associated metric of this spacetime is a static Lorentzian wormhole and it includes the Schwarzschild black hole, a family of naked singularity and a disjoint family of Lorentzian wormholes. Calculate the energy content of this tetrad field using the gravitational energy-momentum given by M{\o}ller in teleparallel spacetime we find that the resulting form depends on the arbitrary function and does not depend on the two parameters $k_1$ and $k_2$ characterize the wormhole. Using the regularized expression of the gravitational energy-momentum we get the value of energy does not depend on the arbitrary function.Comment: 11 pages Late

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