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

Two spherically symmetric, static Lorentzian wormholes are obtained in tetrad theory of gravitation as a solution of the equation ρ = ρt = 0, where ρ = Tijuiuj, ρt = (Tij − ½Tgij)uiuj and uiui = −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 k1 and k2 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 Møller’s superpotential method in the context of teleparallel spacetime, we find that E = m or 2m, which does not depend on the two parameters k1 and k2 that characterize the wormhole.