A.I. Ode1, I. I. Ewa2*, L. L. Iwa3, M. A. Aliyu1, J. S. Iwa1, A. U. Maisalatee4 and S. R.Tukur2

The modification of Newton dynamical theory of gravitation (NDTG) by Einstein’s geometrical gravitational field equations (EGGFE) do not invalidate Newton dynamical theory of gravitation or require its replacement instead the Einstein’s field equations differs meaningfully from those of the Newton’s field equations only for object moving at relativistic speed. In this article, an exact analytical solution of Einstein’s geometrical gravitational field equation interior to a static homogeneous spherical bodies whose tensor field varies with time and radial distance was constructed and solved. It was observed that within the interior field, the solution converges to Newton dynamical scalar potential which is thus an extremely discovery with the reliance on two arbitrary function. The result obtained in the limit of weak field is equal to laplacian equation which does not differ significantly from Newton dynamical theory of gravitation. The solution further confirms the assumption that Newton dynamical theory of gravitation is a limiting case of Einstein’s geometrical gravitational theory of gravitation.

Keywords : Newton’s theory, Einstein’s theory, Ricci tensor, energy-momentum tensor, general theory of relativity.

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Citation: Ode, A. I. et al., (2025). Interior Solution of Einstein’s Field Equation For a Homogeneous Spherical Massive Bodies Whose Tensor Field Varies in Radial Size and Time Using Riemannian Golden Metric Tensor. I J T C Physics, 6(3):1-3. DOI : https://doi.org/10.47485/2767-3901.1066