Abstract

Schwarzschild solution is the simplest solution of Einstein's field equations, but it has not been able to be describe any non-spherical in shape as in the real are existing. Many objects like stars and/or galaxies are in the form of ellipsoidal form and consequently, the gravitational lines around the objects are different in comparison with spherical form. In this paper a line element has been constructed with the intention, not only to describe a spherical form but also to explain an ellipsoidal system in more accurate and complete form. In fact, Schwarzschild line element and its solution is only a part of the whole work, which I have done. Applying this metric for more consideration an arbitrary object is the next step. The solution for planetary orbit of an ellipsoid planet by using Einstein’s field equations has also been done. We attempt to solve these equations as the exterior solution for an ellipsoidal planet.

Key words: General relativity, Schwarzschild-like solution, elliptical stars, planetary orbits.