  We investigate the geometrical properties, spectral classification,
geodesics, and causal structure of the Bonnor's spacetime [Journal of Physics A
Math. Gen., \textbf{10}, 1673 (1977)], i.e., a stationary axisymmetric solution
with a rotating dust as a source. This spacetime has a directional singularity
at the origin of the coordinates (related to the diverging vorticity field of
the fluid there), which is surrounded by a toroidal region where closed
timelike curves (CTCs) are allowed, leading to chronology violations. We use
the effective potential approach to provide a classification of the different
kind of geodesic orbits on the symmetry plane as well as to study the
helical-like motion aroud the symmetry axis on a cylinder with constant radius.
In the former case we find that as a general feature for positive values of the
angular momentum test particles released from a fixed space point and directed
towards the singularity are repelled and scattered back as soon as they
approach the CTC boundary, without reaching the central singularity. In
contrast, for negative values of the angular momentum there exist conditions in
the parameter space for which particles are allowed to enter the pathological
region. Finally, as a more realistic mechanism, we study accelerated orbits
undergoing friction forces due to the interaction with the background fluid,
which may also act in order to prevent particles from approaching the CTC
region.
