A strictly geometric interpretation of gravitation in general relativity

Abstract

A geometric interpretation of gravitation is given using general relativity. The law of gravitation is taken in the formR ₄₄=0, whereR ₄₄is the component of the contracted Riemann-Christoffel (Ricci) tensor representing the curvature of time. The remaining curvature components of the contracted Riemann-Christoffel tensor may or may not vanish. All that is required in addition toR ₄₄=0 is that the Gaussian curvatureR be nowhere infinite. The conditionR ₄₄=0 yields a nonlinear wave equation. One of the static degenerate solutions represents the gravitational field surrounding a static gravitational point singularity. It is found that for this solution, the three famous predictions of general relativity are obtained in the weak-field approximation. In addition, it is found that there is a correction to the Kepler period of revolution for an orbit.