Energy-momentum distribution: A crucial problem in general relativity

This paper is aimed to elaborate the problem of energy-momentum in general relativity. In this connection, we use the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Moller to compute the energy-momentum densities for two exact solutions of Einstein field equations. The space-times under consideration are the nonnull EinsteinMaxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Godel solution and the Godel metric become special cases of the nonnull Einstein-Maxwell solutions. It turns out that these prescriptions do not provide consistent results for any of these space-times. These inconsistent results verify the well-known proposal that the idea of localization does not follow the lines of pseudotensorial construction but instead follows from the energy-momentum tensor itself. These differences can also be understood with the help of the Hamiltonian approach.