Energy–momentum localization for Bianchi type-IV Universe in general relativity and teleparallel gravity

Abstract

In this study we have investigated the energy–momentum distributions for homogeneous and anisotropic Bianchi type-IV in B class Universe. For this purpose, we have used energy–momentum complexes of Einstein, Bergmann–Thomson, Landau–Lifshitz (LL), Papapetrou, Tolman and Moller in general relativity (GR) is also Einstein, Bergmann–Thomson, Landau–Lifshitz and Moller in teleparallel gravity (TG). From the obtained results we have found that Einstein and Bergmann–Thomson distributions are exactly giving the same results in GR and TG but the Landau–Lifshitz, Papapetrou Tolman and Moller energy–momentum distributions do not provide the same results with Einstein and Bergmann–Thomson in GR and TG. Furthermore, Einstein, Bergmann–Thomson and LL results are the same in different gravitation theories and we get that both GR and TG are equivalent theories for these prescriptions. From the obtained solutions, we could say that these are equivalent theories. Also, Moller energy–momentum distributions do not give the same results in GR and TG. However, we have found that all energy prescriptions are negative and our results agree with Nester et al.