Motion of Particles in Einstein's Relativistic Field Theory. V. Gravitation and the Lorentz-Covariant Procedure

Abstract

In several earlier papers the author developed an approximation method for finding the Lorentz-covariant equations of structure and motion of interacting particles (represented by singularities) in Einstein's theory of the nonsymmetric field. In these earlier papers two specific procedures were suggested for investigating a particular form of partial differential equation which appears when carrying out the approximation method. One of these two specific procedures was Lorentz-covariant at each stage of the analysis and one was not. In both cases the final result was Lorentz-covariant. In the earlier papers, when applying the approximation method to specific particles, only the noncovariant procedure was used. In this paper we illustrate the use of the Lorentz-covariant procedure by applying this procedure up to fourth order to the case of interacting simple neutral particles—particles which interact only through the gravitational field.