ENERGY–MOMENTUM DISTRIBUTION: A CRUCIAL PROBLEM IN GENERAL RELATIVITY

Abstract

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 Möller to compute the energy–momentum densities for two exact solutions of Einstein field equations. The space–times under consideration are the nonnull Einstein–Maxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Gödel solution and the Gödel 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.