Astrophysically Satisfactory Solutions to Einstein's R-33 Gravitational Field Equations Exterior/Interior to Static Homogeneous Oblate Spheroidal Masses

n this article, we formulate solutions to Einstein’s geometrical field equations derived using our new approach. Our field equations exterior and interior to the mass distribu- tion have only one unknown function determined by the mass or pressure distribution. Our obtained solutions yield the unknown function as generalizations of Newton’s grav- itational scalar potential. Thus, our solution puts Einstein’s geometrical theory of grav- ity on same footing with Newton’s dynamical theory; with the dependence of the field on one and only one unknown function comparable to Newton’s gravitational scalar po- tential. Our results in this article are of much significance as the Sun and planets in the solar system are known to be more precisely oblate spheroidal in geometry. The oblate spheroidal geometries of these bodies have effects on their gravitational fields and the motions of test particles and photons in these fields