Finslerian post-Riemannian corrections to the equations of geodesics

Abstract

The generalization of the ordinary hypothesis of Riemannian geodesics for test bodies motion to the hypothesis of Finslerian geodesies gives rise to observable consequences which can explicitly be described in the case of the static gravitational field. The Finslerian corrections prove to be those in the velocity of motion and lead, in particular, to centennial changes in the eccentricities of the planetary orbits. The residual change in the eccentricity of the Mercurian orbit unexplainable by the Riemannian post-Newtonian corrections is used to estimate the order of a characteristic Finslerian parameter.