Geodesics on non-Riemannian Geometric theory of Planar Defects

TL;DR

This paper uses Hamilton-Jacobi methods to analyze geodesics around non-Riemannian planar torsional defects, revealing how torsion influences geodesic paths and models a gravitationally repulsive domain wall.

Contribution

It introduces a novel approach to study geodesics in non-Riemannian geometry with torsion, linking geometric defects to physical phenomena.

Findings

Geodesics form parabolas influenced by torsion.

In defect-free cases, geodesics are straight lines.

Torsion acts as a Burgers vector, affecting geodesic behavior.

Abstract

The method of Hamilton-Jacobi is used to obtain geodesics around non- Riemannian planar torsional defects.It is shown that by perturbation expansion in the Cartan torsion the geodesics obtained are parabolic curves along the plane x-z when the wall is located at the plane x-y.In the absence of defects the geodesics reduce to straight lines.The family of parabolas depend on the torsion parameter and describe a gravitationally repulsive domain wall.Torsion here plays the role of the Burgers vector in solid state physics.