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.