A new boundary condition and the geodesic postulate

Abstract

Einstein and Rosen have admitted that the geodesic postulate is an extraneous one and that the field-equations of gravitation must give both matter and motion independently of such a postulate. It has not been rigorously proved yet that the geodesic postulate is implicit in the field-equations. A new boundary condition is stated here, couched in invariant terms; it is found to be satisfied by the Schwarzschild solution, and the content of the geodesic postulate that a test-particle describes a geodesic is shown to be implied by this condition. No extraneous postulate is necessary to account for the motion if the new boundary condition is accepted.