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 Moller 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 Moller 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.
Highlights
Since the outset of the general theory of relativity, the notion of energy-momentum localization has been one of the thorniest problems, which remains unsolved
We study the spacial cases of non-diagonal Bianchi type space-time Bianchi type-II (BII), Bianchi type-VIII (BVIII) and Bianchi type-IX (BIX)
We found that the energy density component in Møller prescription is zero for all Bianchi types space-times in General relativity (GR)
Summary
Since the outset of the general theory of relativity, the notion of energy-momentum localization has been one of the thorniest problems, which remains unsolved. Aydogdu and Salti [42] calculated the energy-momentum density for Bianchi type-II space time with the Bergmann-Thomson energy momentum definitions in both general relativity and teleparallel gravity and they found that these two gravitational theories give the same result which is that total energy is equal to zero. Tripathy et al [43] they obtained energy and momentum distributions for the spatially homogeneous and anisotropic Bianchi type VIh metric, they used Einstein, Landau-Lifshitz, Papapetrou, and Bergmann-Thompson complexes in the framework of general relativity. Özkurt and Aygün [44] investigated the energy and momentum density homogeneous Bianchi type VIh metric with Einstein, Bergmann-Thomson, Landau-Lifshitz, Papapetrou, Tolman and Møller prescriptions in general relativity and teleparallel gravity and their results agree with Tripathyet and Tryon.
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