Bi-connected Gravity Fields

TL;DR

This paper introduces a bi-connection formalism of General relativity that utilizes both the Weitzenböck and Levi-Civita connections to clarify the geometric structure of spacetime.

Contribution

It presents a novel formalism combining dual connections in General relativity, providing clearer tensor representations of geodesic and loxodromic equations.

Findings

Clarifies the joint meaning of geodesic and loxodromic equations.

Provides explicit tensor formulations for the dual-connection approach.

Enhances understanding of the geometric structure of gravity theories.

Abstract

I describe a bi-connection formalism of General relativity based on the dual role of the Weitzenb\"{o}ck connection defining the parallelism at a distance and the concomitant Levi-Civita connection derived from the Riemannian metric. A more explicit tensor writing of the geodesic and loxodromic equations clarifies their joint meaning.