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$\text{}_{1}$, k$\text{}_{2}$ of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation ρ= ρ$\text{}_{t}$=0 with ρ=T$\text{}_{i,j}$u$\text{}^{i}$u$\text{}^{j}$, ρ$\text{}_{t}$ =(T$\text{}_{ij}$-1/2Tg$\text{}_{ij}$) u$\text{}^{i}$u$\text{}^{j}$, where u$\text{}^{i}$u$\text{}_{i}$=-1. From this solution which contains an arbitrary function we can generate the other two solutions obtained before. The associated metric of this space-time is a static Lorentzian wormhole and it includes the Schwarzschild black hole, a family of naked singularity and a disjoint family of Lorentzian wormholes. Calculating the energy content of this tetrad field and using the gravitational energy momentum given by Møller in the teleparallel space-time we find that the resulting form depends on the arbitrary function and does not depend on the two parameters k$\text{}_{1}$ and k$\text{}_{2}$ characterizing the wormhole. Using the regularized expression of the gravitational energy momentum we get the value of energy which does not depend on the arbitrary function.