  This work deals with the analysis of cylindrically symmetric and stationary
space-times $\mathcal{C}_{t}$ with closed timelike curves. The equation of
motion describing the evolution of a massive scalar field in a
$\mathcal{C}_{t}$ space-time is obtained. A class of space-times with closed
timelike curves describing cosmic strings and cylinders is studied in detail.
In such space-times, both massive particles as well as photons can reach the
non-causal region. Geodesics and closed timelike curves are calculated and
investigated. We have observed that massive particles and photons describe,
essentially, two kinds of trajectories: confined orbits and scattering states.
The analysis of the light cones show us clearly the intersection between future
and past inside the non-causal region. Exact solutions for the equation of
motion of massive scalar field propagating in cosmic strings and cylinder
space-times are presented. Quasinormal modes for the scalar field have been
calculated in static and rotating cosmic cylinders. We found unstable modes in
the rotating cases. Rotating as well as static cosmic strings, i.e., without
regular interior solutions, do not display quasinormal modes for the scalar
field. We conclude presenting a conjecture relating closed timelike curves and
space-time instability.
