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Alofi, A. and Gad, R.M. (2019) On Torsion Axial Vector and Gravitational Energy in Lewis-Papapetrou Space-Time in the Theory of Teleparallel Gravity. arXiv preprint arXiv:1912.06653.

has been cited by the following article:

• TITLE: Energy-Momentum Density of Non-Diagonal Bianchi Type Space-Time in General Relativity and Teleparallel Gravity

  AUTHORS: Ragab M. Gad, Haifaa A. Alharbi

  KEYWORDS: Energy-Momentum Densities, Double Index Complexes, Teleparallel Gravity, Bianchi Type Space Time

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.9, September 28, 2021

  ABSTRACT: We calculated the energy-momentum density of non-diagonal Bianchi type space-time in two different theories of gravity, General relativity (GR) and the theory of Teleparallel gravity (TG). Firstly, by applying Einstein, Landau-Lifshitz, Bergmann-Thomson and Møller prescriptions, using double index complexes in GR. Secondly, in the frame work of TG, we used the energy momentum complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. We also study the spacial cases of non-diagonal Bianchi type space-time BII, BVIII and BIX. We obtained the same energy-momentum density components for Einstein and Bergmann-Thomson prescriptions for the above four mentioned space-times that we considered in our work. Also, we found that the energy density component in Møller prescription is zero for all Bianchi types space-times in GR. Furthermore, we show that if the metric components are functions of time t alone, then the total gravitational energy is identically zero.