Einstein’s equations of motion for test particles exterior to spherical distributions of mass whose tensor field varies with time, radial distance and polar angle

In this article the metric tensor exterior to hypothetical spherical distributions of mass whose tensor field varies with time, radial distance and Polar angle is extended to derive equations of motion for test particles in the gravitational field. The time equation is used to derive the expression for the variation of the time on a clock moving in this gravitational field. For pure polar motion, test particles move with velocity that has an inverse dependence on the radial distance. The results show that the introduction of q in this field does not alter the inverse dependence of velocity on the radial distance.