Teleparallel version of the Levi–Civita vacuum solutions and their energy contents

Abstract

In this paper, we find the teleparallel version of the Levi–Civita metric and obtain tetrad and the torsion fields. The tensor, vector, and the axial-vector parts of the torsion tensor are evaluated. It is found that the vector part lies along the radial direction only while the axial-vector vanishes everywhere because the metric is diagonal. Further, we use the teleparallel version of Moller, Einstein, Landau–Lifshitz, and Bergmann–Thomson prescriptions to find the energy-momentum distribution of this metric and compare the results with those already found in General Relativity (GR). It is worth mentioning here that momentum is constant in both of the theories for all the prescriptions. The energy in teleparallel theory is equal to the corresponding energy in GR only in the Moller prescription for the remaining prescriptions, the energy does not agree in both theories. We also conclude that Moller's energy-momentum distribution is independent of the coupling constant λ in the teleparallel theory.PACS Nos.: 04.20.–q, 04.20.Cv