Einstein’s Field Equation Extension for Spherical Fields with Tensor Variation in time and Radial Distance

In this article, we applied the Riemannian Geometry of space-time and obtained the affine connection coefficient, Riemann Christofell tensor, Ricci tensor and an extended Einstein’s field equation for spherical fields. The obtained result reduces to corresponding pure Newtonian indicating that an agreement with the equivalence principle in Physics. It contains correction term that not in the Newton’s dynamical theory or Einstein’s geometrical theory of gravitation. The consequence of the correction term is that it can be applicable to the determination of the existence of gravitational waves.