The infeld/schild approach to the geodesic motion of test particles in general relativity

Test particles are defined and a version of the Infeld/Schild theorem on geodesic motion is presented. The hypotheses of the theorem are discussed in the IPN approximation and in the Weyl static axisymmetric metrics. Initial terms in a series solution of the linearized field equations are found explicitly for a test particle on an arbitrary timelike geodesic.