Totally Asymmetric Torsion on Riemann-Cartan Manifold

TL;DR

This paper introduces a relativistic theory on Riemann-Cartan manifolds featuring a naturally arising totally antisymmetric torsion, which aligns autoparallel curves with metric geodesics without arbitrary assumptions.

Contribution

It presents a novel relativistic framework on Riemann-Cartan manifolds where totally antisymmetric torsion emerges naturally, unifying autoparallel and geodesic curves.

Findings

Totally antisymmetric torsion appears naturally in the theory.

Autoparallel curves coincide with metric geodesics.

The theory does not require ad hoc assumptions.

Abstract

A relativistic theory constructed on Riemann-Cartan manifold with a derived totally antisymmetric torsion is proposed. It follows the coincidence of the autoparallel curve and metric geodesic. The totally antisymmetric torsion naturally appears in the theory without any ad hoc imposed on.