Geodesic motion around traversable wormholes supported by a massless conformally-coupled scalar field

TL;DR

This paper analyzes the geodesic motion in a specific traversable wormhole spacetime supported by a conformally-coupled scalar field, providing analytical solutions and exploring orbit types and their dependencies.

Contribution

It presents an analytical study of geodesic equations in a wormhole spacetime with a conformally-coupled scalar field, revealing unique orbit behaviors.

Findings

Bound orbits for time-like geodesics occur only in one universe.

No time-like two-world bound orbits exist under any conditions.

Analytical solutions are expressed using Weierstraß functions.

Abstract

We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the JNWW spacetime. We study the geodesic motion of time-, light- and space-like particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstra\ss \ functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for time-like geodesics only in one of the two worlds. Moreover, under no conditions there exist time-like two world bound orbits.