Energy in Reboucas-Tiomno-Korotkii-Obukhov and Godel-type space-times in Bergmann-Thomson's formulations

Abstract

We calculate the total energy (the matter plus fields) of the universe considering Bergmann-Thomson's energy-momentum formulation in both Einstein's theory of general relativity and tele-parallel gravity on two different space-times; namely Reboucas-Tiomno-Korotkii-Obukhov and the Godel-type metrics. We also compute some kinematical quantities for these space-times and find that these space-times have shear-free expansion and non-vanishing four-acceleration and vorticity. Different approximations of the Bergmann-Thomson energy-momentum formulation in these different gravitation theories give the same energy density and agree with each other. The results advocate the importance of energy-momentum definitions.