Self-dual Lorentzian wormholes and energy in teleparallel theory of gravity

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Two spherically symmetric, static Lorentzian wormholes are obtained in tetrad theory of gravitation as a solution of the equation ρ = ρ t = 0, where ρ = T ij u i u j , ρ t = (T ij − ½Tg ij )u i u j and u i u i = −1. This equation characterizes a class of spacetime which are “self-dual” (in the sense of electrogravity duality). The obtained solutions are characterized by two parameters k 1 and k 2 and have a common property that they reproduce the same metric spacetime. Thismetric describes a static Lorentzian wormhole and includes the Schwarzschild black hole as a special case. Calculating the energy content of these tetrad fields using Moller’s superpotential method in the context of teleparallel spacetime, we find that E = m or 2m, which does not depend on the two parameters k 1 and k 2 that characterize the wormhole.