On the relative energy associated with space-times of diagonal metrics

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of generalized diagonal metric, we consider the Einstein, Bergmann-Thomson and Landau-Lifshitz energy and/or momentum definitions both in Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We find same energy distribution using Einstein and Bergmann-Thomson formulations, but we also find that the energy-momentum prescription of Landau-Lifshitz disagree in general with these definitions. We also give eight different well-known space-time models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianchi Type-I models all the formulations give the same result. This result agrees with the previous Works of Cooperstock-Israelit, Rosen, Johri et al, Banerjee-Sen, Xulu, Vargas and Salti et al and supports the viewpoints of Albrow and Tryon.