Dynamics in wormhole spacetimes: a Jacobi metric approach

TL;DR

This paper investigates particle dynamics in wormhole spacetimes using the Jacobi metric, revealing stable orbits, the relation between curvature and wormhole structure, and conditions for throat existence.

Contribution

It introduces a novel approach linking Jacobi metric curvature to wormhole geometry and provides a simple test for identifying wormhole throats.

Findings

Identified the only stable circular orbit at the wormhole throat.

Linked Gaussian curvature of the Jacobi metric with the flare-out condition.

Provided a test for detecting wormhole throats using curvature analysis.

Abstract

This article deals with the study of the dynamics of particles in different wormhole geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris-Thorne wormhole. We found the only stable circular orbit located at the throat. We show that the Gaussian curvature of the Jacobi metric is directly related with the wormhole flare-out condition. We provide a simple test for determining the existence of a throat in a spacetime by using the Gaussian curvature of the associated Jacobi metric only. We discuss about the trajectories in the Kepler problem in a wormhole background. Finally, we discuss about the restrictions over the stress-energy tensor imposed by the existence of elliptic orbits in the Kepler problem.