Some examples of different descriptions of energy-momentum density in the context of Bianchi IX cosmological model

TL;DR

This paper compares various energy-momentum definitions in the Bianchi IX cosmological model, revealing differences in energy density calculations and highlighting the non-uniqueness of energy-momentum localization in General Relativity.

Contribution

It provides explicit calculations of energy-momentum densities using five different prescriptions within a specific cosmological model, illustrating their disparities.

Findings

Møller and Weinberg densities are zero for the model.

Different prescriptions yield different non-zero energy-momentum densities.

Supports the idea that energy-momentum definitions are not unique in GR.

Abstract

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, M{\o}ller and Weinberg. The energy densities of M{\o}ller 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.