In this paper, we consider the problem of test particles and test scalar fields propagating on
the background of a class of wormhole space-times. For test particles, we solve for arbitrary
causal geodesics in terms of integrals which are solved numerically. These integrals are
parametrized by the radius and shape of the wormhole throat as well as the initial conditions
of the geodesic trajectory. In terms of these parameters, we compute the conditions for the
geodesic to traverse the wormhole, to be reflected by the wormhole's potential or to be …

In Sec. III of our paper, we considered the stability of solutions of the scalar wave equation
on a class of wormhole backgrounds. Whether or not the solutions are stable depends on
the value of the coupling of the scalar to the background curvature. We showed that these
regions of instability are related to an infinite set of spurious poles in the expression for the
self-force on a scalar charge held static in these wormhole spacetimes. Specifically, all the
values of the coupling constant for which the self-force diverges lie outside the domain of …