The geodesic postulate in general relativity

Abstract

It is argued that the geodesic postulate is not implicit in the relativity equations. A certain indeterminacy about the motion of the particle in Schwarzschild's solution is indicated. If the field equations are also to give the motion as suggested by Einstein the geodesic postulate must be abandoned, in which case the difficulty still remains whether a singularity in a solution does represent a mass-particle or not. If the geodesic postulate is to be retained, and if at the same time Einstein's suggestion is accepted, then certain tracks must reduce to geodesics in the limit, provided the singularities represent masses. This may serve as a test whether a singularity represents a mass or not.