Geodesic analysis and steady accretion on a traversable wormhole

In this work, we analyze the behavior of light and matter as they pass near and through a traversable wormhole throat. In particular, we study the trajectories of massive and massless particles and the dust accretion around a traversable wormhole previously reported in Rueda et al. (2022). For massive particles, we integrate the trajectory equation for ingoing and outgoing geodesics and classify the orbits of particles scattered by the wormhole in accordance with their asymptotic behavior far from the throat. We represent all the time-like trajectories in an embedding surface where it is shown explicitly the trajectories of (i) particles that deviate from the throat and remain in the same universe, (ii) particles that traverse the wormhole to another universe, and (iii) particles that get trapped in the wormhole in unstable circular orbits. For the massless particles, we numerically integrate the trajectory equation to show the ray-tracing around the wormhole specifying the particles that traverse the wormhole and those that are only deviated by the throat. For the study of accretion, we consider the steady and spherically symmetric accretion of dust. Our results show that the wormhole parameters can significantly affect the behavior of light and matter near the wormhole. Some comparisons with the behavior of matter around black holes are made.