On a nonlinear and Lorentz-invariant version of Newtonian gravitation

Abstract

The Newtonian theory of gravitation is modified to include the gravitational energy as a source of gravitational potential, thus making the theory self-coupled and nonlinear. The modified theory can be derived from a Lorentz-invariant action principle. The Kepler problem is discussed in this theory and it is shown that the perihelion of the orbit steadily precesses. The rate of precession is, however, insufficient to account for the observed precession of the perihelion of Mercury. The differences from the Newtonian theory for the bending of light and the gravitational redshift of spectral lines are shown to be marginal.