  We discuss several properties of static, spherically symmetric wormholes with
particular emphasis on the behavior of causal geodesics and the propagation of
linear fields. We show there always exist null geodesics which are trapped in a
region close to the throat. Depending upon the detailed structure of the
wormhole geometry, these trapped geodesics can be stable, unlike the case of
the Schwarzschild black hole. We also show that test scalar fields propagating
on such wormholes are stable. However, when a mixture of ghost and Klein-Gordon
scalar fields is used as a source of the Einstein equations we prove that the
resulting static, spherically symmetric wormhole configurations are linearly
unstable.
