A simple special relativistic perturbation scheme for yielding the general relativistic behavior of point particles and photons in the gravitational field of stars

Abstract

Using the principle of the equivalence of mass and energy of the special theory of relativity, it is shown that a Lagrangian yielding the same equations of motion that Einstein originally derived for the precession of the perihelion of Mercury and the bending of light by the sun may be derived by using a new perturbation scheme applied to the Lagrangian for an orbiting point particle. The magnitude of the Newtonian potential energy term appearing in the Lagrangian of an orbiting point particle is divided by c2 to yield a first-order mass correction to the potential energy. The corrected first-order potential energy term is in turn divided by c2 to yield a second-order mass correction to the total potential energy, and so forth. Successive correction terms are shown to yield successively smaller mass corrections to the total potential energy. This scheme, up to the first-order term in perturbation, leads to the astronomically observed corrections to the advance of the perihelion of Mercury and the bending of light by the sun attributable to general relativistic effects.