TY - JOUR
T1 - A tetrad approach to charged fluid motion in the Einstein—Maxwell theory
JF - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO - Proc R Soc Lond A Math Phys Sci
SP - 79
LP - 91
M3 - 10.1098/rspa.1975.0013
VL - 342
IS - 1628
AU -
Y1 - 1975/02/25
UR - http://rspa.royalsocietypublishing.org/content/342/1628/79.abstract
N2 - 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 Γσμv with the Ricci rotation coefficients γαbc 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 ui, (ii) Maxwell’s equations appear as linear relations between the γabc, and (iii) the equations of motion of the source consist of one differential relation and three algebraic relations between the yabc, and the ui. 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.
ER -