Geodesic-invariant equations of gravitation

TL;DR

This paper proposes a gravitational theory invariant under geodesic mappings, addressing the gauge invariance issue in Einstein's equations by treating geodesic mappings as gauge transformations.

Contribution

It introduces a new formulation of gravitation equations that are invariant under geodesic mappings, unlike Einstein's equations.

Findings

Einstein's equations are not invariant under geodesic mappings.

A new theory treats geodesic mappings as gauge transformations.

The proposed theory maintains invariance under these mappings.

Abstract

Einstein's equations of gravitation are not invariant under geodesic mappings, i. e. under a certain class of mappings of the Christoffel symbols and the metric tensor which leave the geodesic equations in a given coordinate system invariant. A theory in which geodesic mappings play the role of gauge transformations is considered.