Minimally relativistic Newtonian gravity

Abstract

Special relativity is introduced into the theory of Newtonian gravity in a systematic manner. The modifications of Newtonian gravity that are made can be seen to be minimal for special relativistic covariance. Space is assumed to be flat. Particle trajectories are determined from a Hamiltonian formulation with a tensor potential hμν. The tensor nature of the potential is justified by requiring Lorentz covariance alone. Nongeneral relativistic field equations for the hμν are obtained. The static, spherically symmetric solutions of these equations are shown to produce the correct values for the precession of the orbit of Mercury and the bending of light near the Sun.