Wormhole Solution and Energy in Teleparallel Theory of Gravity |

G. G. L. Nashed
Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt |

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Received: 10 12 2006; |

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 ρ=ρ_{t}=0 with ρ=T_{i,j}u^{i}u^{j}, ρ_{t} = (T_{ij}-1/2Tg_{ij}) u^{i}u^{j}, where u^{i}u_{i}=-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 k_{1} and k_{2} 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. |

DOI: 10.12693/APhysPolA.111.201 PACS numbers: 04.20.Cv, 04.50.+h, 04.20.-q |