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

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 Janis-Newman-Winicour-Wyman spacetime. We study the geodesic motion of timelike, lightlike, and spacelike 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 timelike geodesics only in one of the two worlds. Moreover, under no conditions there exist timelike two world bound orbits.

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