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.

中文翻译：

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虫洞时空动力学：雅可比度量方法

本文研究了不同几何形状的虫洞中的测地线运动。使用雅可比度量方法，我们研究了具有不同类型红移函数的 Morris-Thorne 虫洞上的测地线运动。我们还通过使用所谓的 Eisenhart-Duval 升力对度量进行修改来研究动态虫洞中的测地线运动。我们在虫洞背景下解决二维开普勒问题。使用高斯曲率（取决于能量），我们提供了轨迹分类。我们证明了耀斑条件与高斯曲率有关。