# 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.

## Key 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.