Research of Gravitation in Flat Minkowski Space

TL;DR

This paper proposes an alternative theory of gravitation within flat Minkowski space using an antisymmetric tensor, achieving results consistent with General Relativity for phenomena like light deflection and perihelion shift.

Contribution

It introduces a non-linear connection based on an antisymmetric tensor in flat spacetime, matching GR's predictions for key gravitational effects.

Findings

Results for light deflection and perihelion shift match GR.

Equations of motion differ from EIH by Lorentz-invariant terms.

Barycenter calculations are consistent with GR.

Abstract

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession, i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the $n$-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order $c^{-2}$.