Higher-dimensional energy–momentum problem for Bianchi types V and I universes in gravitation theories

Abstract

Using the Einstein, Bergmann–Thomson, Landau–Lifshitz, Møller, Papapetrou and Tolman energy–momentum complexes in general relativity (GR) and teleparallel gravity (TG), we calculate the total energy–momentum distributions associated with N-dimensional Bianchi type V universe. While the solutions of Einstein, Bergmann–Thomson and Tolman energy and momentum densities are the same as each other, the solutions of Landau–Lifshitz, Møller and Papapetrou energy–momentum densities are different for N-dimensional Bianchi type V space-time in GR and TG. Obtained results for Einstein, Bergmann–Thomson and Landau–Lifshitz definitions we could say that GR and TG are in the same class. Because different energy–momentum distributions provide same results. However we have discussed N-dimensional Bianchi type I solutions and then we obtained all energy–momentum solutions are vanish in GR and TG theories. These results agree with Banerjee–Sen, Xulu, Aydoḡdu–Saltı and Radinschi in four dimensions.