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Modification of The Interior Solution of Einstein's G22 Field Equation for A Homogeneous Spherical Massive Bodies Whose Fields Differ in Radial Size, Polar

Rilwan Usman1*, Abba Umar Maisalatee2, M. Alpha3

In the general theory of relativity, Einstein’s field equations relate the geometry of space-time with the distribution of matter within it. Research has shown that the tensors for spherical massive bodies are not functions of radial distance only as shown by Schwarzchild; they depend on other factors such as polar angle, azimuthal angle, and time. In this article, we formulate the analytical solution of Einstein’s field equation interior to a homogeneous spherical body whose tensor field varies with time, radial distance, and polar angle using weak field and slow-motion approximation. The obtained result converges to Newton’s dynamical scalar potential with additional time factors not found in the well-known Newton’s dynamical theory of gravitation which is a profound discovery with the dependency on three arbitrary functions. The result obtained can be used in the study of rotating astrophysical bodies such as stars. Our result obeyed the equivalence principle of Physics.