A tetrad approach to charged fluid motion in the Einstein—Maxwell theory

Abstract

By projecting the fluid flow vector on to a unique tetrad of eigenvectors of the electromagnetic part of the energy-momentum tensor, the Einstein-Maxwell equations for a charged fluid space-time in four dimensions may be simplified and reduced to a system which determines the functional dependence of the eigenvectors. This is achieved by replacing the Riemannian connexion Γ σ μv with the Ricci rotation coefficients γ α bc which describe the tetrad geometry. In the anholonomic reference system of the tetrad it is shown that (i) the fluid flow vector has at most two non-zero components u i , (ii) Maxwell’s equations appear as linear relations between the γ a bc , and (iii) the equations of motion of the source consist of one differential relation and three algebraic relations between the y a bc , and the u i . As an example, the problem of determining a time-dependent magnetosonic-gravitational wave is shown to be reducible to that of solving a well-known type of nonlinear second order ordinary differential equation.