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 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.

Electromagnetic solitary waves in magnetized plasmas

A Hamiltonian formulation, in terms of a non-canonical Poisson bracket, is presented for a nonlinear fluid system that includes reduced magnetohydro-dynamics and the Hasegawa–Mima equation as limiting cases. The single-helicity and axisymmetric versions possess three nonlinear Casimir invariants, from which a generalized potential can be constructed. Variation of the generalized potential yields a description of exact nonlinear stationary states. The new equilibria, allowing for plasma flow as well as partial electron adiabaticity, are distinct from those found in conventional magnetohydrodynamic theory. They differ from electrostatic stationary states in containing plasma current and magnetic field excitation. One class of steady-state solutions is shown to provide a simple electromagnetic generalization of drift-solitary waves.