Gravitomagnetism, Coupling, Scalar Potential, Vector potential, Riemann’s Laplacian Operator

In this article, the generalized Schwarzschild metric for time varying spherical fields is used to derive equations of motion for test particles in the vicinity of a time varying spherical mass. A generalized gravitational scalar potential is expanded and used to construct equations of motion for test particles exterior to a time varying spherical distribution of mass. The world line element at the equatorial plane of a spherical massive body was constructed. This was used to study the motion of photons. The equations of motion obtained have additional terms not found in equivalent equations in the Schwarzschild’s field. These are uncovered for theoretical and astrophysical development and applications. Remarkably, when the time varying scalar gravitational potential reduces to that of a static field, results obtained in Schwarzschild's field are obtained. Thus, our generalization is mathematically satisfactory and has astrophysical implications for the study of time varying spherical gravitational fields.