  Strong lensing is one of the most direct probes of the mass distribution in
the inner regions of galaxy clusters. It can be used to constrain the density
profiles and to measure the mass of the lenses. Moreover, the abundance of
strong lensing events can be used to constrain the structure formation and the
cosmological parameters through the so-called "arc-statistics" approach.
However, several issues related to the usage of strong lensing clusters in
cosmological applications are still controversial, leading to the suspect that
several biases may affect this very peculiar class of objects. With this study
we aim at better understanding the properties of galaxy clusters which can
potentially act as strong lenses. We do so by investigating the properties of a
large sample of galaxy clusters extracted from the N-body/hydrodynamical
simulation MareNostrum Universe. We explore the correlation between the cross
section for lensing and many properties of clusters, like the mass, the
three-dimensional and projected shapes, their concentrations, the X-ray
luminosity and the dynamical activity. We find that the probability of strong
alignments between the major axes of the lenses and the line of sight is a
growing function of the lensing cross section. In projection, the strong lenses
appear rounder within R200, but we find that their cores tend to be more
elliptical as the lensing cross section increases. We also find that the
cluster concentrations estimated from the projected density profiles tend to be
biased high. The X-ray luminosity of strong lensing clusters is higher than
that of normal lenses of similar mass and redshift. This is particular
significant for the least massive lenses. Finally, we find that the strongest
lenses generally exhibit an excess of kinetic energy within the virial radius,
indicating that they are more dynamically active than usual clusters.
