Some examples of different descriptions of energy-momentum density in the context of Bianchi IX cosmological model
Based on the Bianchi type IX metric, we calculate the energy and momentum density components of the gravitational field for the five different definitions of energy-momentum, namely, Tolman, Papapetrou, Landau-Lifshitz, Møller and Weinberg. The energy densities of Møller and Weinberg become zero for the spacetime under consideration. In the other prescriptions, i.e., Tolman, Papapetrou and Landau-Lifshitz complexes, we find different non-vanishing energy-momentum densities for the given spacetime, supporting the well-known argument in General Relativity that the different definitions may lead to different distributions even in the same spacetime background.
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