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

G. G.L. Nashed, Ain Shams University

Abstract

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 - 1/2Tgij)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. © Pleiades Publishing, Ltd., 2009.