keywords: Einstein Theory, General Theory, Newtonian Theory, Scalar Potential, Spherical Mass, Time Dilation and Riemannian Theory
Einstein’s geometrical theory of gravitational is the most accredited theory for explaining time dilation. In this paper the General Dynamical Theory of Gravitation and extended Newtonian gravitational scalar potential exterior to static homogeneous spherical mass is used to study the gravitational time dilation. A new extended equation with more correction terms for gravitational time dilation was obtained. The obtained extended expression for gravitational time dilation reduces to exactly pure Einstein expression to the order of 𝑐 0 and to the order of 𝑐 −2 it contains additional correction terms. The significance of the results obtained is that they reduce to the well - known results in weak field approximations. This indicates that the Riemannian extension is mathematically sound and agrees with well-known astrophysical facts. The new expression for the gravitational time dilation can be incorporated in the design of global positioning systems to improve their precision rate.