Wormhole solution and Energy in Teleparallel Theory of Gravity

Abstract

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 $\rho =T_{i,j}{u}^i{u}^j$, ${\rho }_t=(T_{ij}-\frac{1}{2}T{g}_{ij})u^i{u}^j$ where $u^i{u}_i=-1$. 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 Møller 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.

11 pages Latex