The Precession of Perihelion over Modification of Newton Gravity

Abstract

In this paper the idea is revised how the metric in flat Minkowskian spacetime gets transformed from one coordinates system to another after successive Lorentz transformations. And likewise this idea is generalized to achieve the metric transformation from one curved spacetime to another. The introduction of mass perturbed the initial flat space time in to curved spacetime, here the corresponding perturbed metric assumed as point-to-point infinitesimal quasi Lorentz transformation of the Minkowski metric. For multiple sources the manifestation of perturbed metric is formulated performing the successive quasi-Lorentz transformations in non-Euclidean curved spacetime. This interactive model for multiple sources of nonlinear perturbation reveals a clear shift from Newtonian gravity. In case of gravity the synergy among the sources is obvious; interestingly this formula is checked in retrieving the unstable planetary elliptical orbit and the precession of perihelion for two body planetary systems that verifies the model.