Modified schwarzschild solution for an oblate spheroidal body

Abstract

Most stars and planets including the sun are not perfect spheres, but these are oblate spheroidal bodies in practice. In the theory of general relativity, this real structure and it``s related phenomena requires the Schwarzschild solution of Einstein field equation for a perfect spheroidal body to be modified. Being the spherical symmetry of gravitational source which is one of the three assumptions for the Schwarzschild solution abandoned, the oblate spheroidal coordinate is applied to solve it. In this work, the approximate solution is obtained and the new correction terms in the augular precession $\Delta \phi_m 100 = 6 \pi{GMN} (1-\triangle^2)/c^2(1+e)a_{\min}\, \cosh \eta$ and the light deflection $\Delta \phi = \frac{1}{1+\triangle}(4GM/c^2a_{\min} \cosh \eta + \pi \triangle/2)$ are calculated respectively.