Wormhole solution and energy in teleparallel theory of gravity

G. G.L. Nashed, Ain Shams University

Abstract

An exact solution is obtained in the tetrad theory of gravitation. This solution is characterized by two parameters k1, k2 of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation ρ = ρt = 0 with ρ = T i,juiuj, ρt = (Tij - 1/2Tgij)uiuj, where uiui = -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 k1 and k2 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.