Motion of Particles in Einstein's Relativistic Field Theory. III. Coordinate Conditions

Abstract

In two earlier papers the author developed an approximation procedure for finding the Lorentz-covariant equations of structure and motion of interacting particles (represented by singularities) in Einstein's theory of the nonsymmetric field and in Einstein's theory of the gravitational field. In the earlier papers the author worked exclusively in a specific set of coordinate systems, the harmonic coordinate systems. In this paper the author shows that the procedure developed in the earlier papers can be used without imposing any conditions on the coordinates except that the fundamental field be the Minkowski metric in the absence of particles. The author also shows that up to any finite order of approximation the use of harmonic coordinates does not reduce the set of invariantly distinct solutions to Einstein's field equations.