Dynamics in wormhole spacetimes: a Jacobi metric approach

This paper deals with the study of geodesic motion in different wormholes geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris-Thorne wormhole with different types of redshift functions. We also study geodesic motion in dynamic wormholes by a modification of the metric with the so called Eisenhart-Duval lift. We solve the 2-dimensional Kepler problem in a wormhole background. Using the Gaussian curvature (depending on energy) we provide a classification of trajectories. We show that the flare-out condition is related with the Gaussian curvature.