The Lukash Plane-Wave Attractor and Relative Energy

We study energy distribution in the context of teleparallel theory of gravity, due to matter and fields including gravitation, of the universe based on the plane-wave Bianchi VII$_{\delta}$ spacetimes described by the Lukash metric. In order to make this calculation we consider the teleparallel gravity analogs of the energy-momentum formulations of Einstein, Bergmann-Thomson and Landau-Lifshitz. We find that Einstein and Bergmann-Thomson prescriptions agree with each other and give the same results for the energy distribution in a given spacetime, but the Landau-Lifshitz complex does not. Energy density turns out to be non-vanishing in all of these prescriptions. It is interesting to mention that the results can be reduced to the already available results for the Milne universe when we write $\omega=1$ and $\Xi^2=1$ in the metric of the Lukash spacetime, and for this special case, we get the same relation among the energy-momentum formulations of Einstein, Bergmann-Thomson and Landau-Lifshitz as obtained for the Lukash spacetime. Furthermore, our results support the hypothesis by Cooperstock that the energy is confined to the region of non-vanishing energy-momentum tensor of matter and all non-gravitational fields, and also sustain the importance of the energy-momentum definitions in the evaluation of the energy distribution associated with a given spacetime