# Teleparallel Version of the Levi-Civita Vacuum Solutions and their Energy Contents - General Relativity and Quantum Cosmology

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Abstract: In this paper, we find the teleparallel version of the Levi-Civita metric andobtain tetrad and the torsion fields. The tensor, vector and the axial-vectorparts of the torsion tensor are evaluated. It is found that the vector partlies along the radial direction only while the axial-vector vanishes everywherebecause the metric is diagonal. Further, we use the teleparallel version ofM$\ddot{o}$ller, Einstein, Landau-Lifshitz and Bergmann-Thomson prescriptionsto find the energy-momentum distribution of this metric and compare the resultswith those already found in General Relativity. It is worth mentioning herethat momentum is constant in both the theories for all the prescriptions. Theenergy in teleparallel theory is equal to the corresponding energy in GR onlyin M$\ddot{o}$ller prescription for the remaining prescriptions, the energy donot agree in both theories. We also conclude that M$\ddot{o}$ller-senergy-momentum distribution is independent of the coupling constant $\lambda$in the teleparallel theory.

Autor: M. Sharif, M. Jamil Amir

Fuente: https://arxiv.org/