  We study strong gravitational lensing in rotating space-times which can be
thought of as realistic galactic models in General Relativity. To this end,
using the Newman-Janis algorithm, we first obtain a rotating version of a
static galactic metric advanced by Bharadwaj and Kar. This is matched with a
generic external Kerr solution without a slowly-rotating approximation. Next,
we construct a rotating version of Perlick's Bertrand space-times and establish
this as a new rotating solution of Einstein's equations where each spatial
radius admits a stable circular orbit. A rotating generalization of a strong
lensing formalism due to Perlick is then applied to the rotating Bharadwaj-Kar
metric and the differences with lensing in the purely Kerr background (for a
Kerr black hole at the galactic center) is pointed out. Then, arguing that a
rotating Bertrand space-time might be a realistic galactic model away from the
galactic center, strong lensing is studied in this situation where the central
singularity is naked. Possible observational signatures are elaborated upon,
which might be useful in distinguishing black holes from naked singularities.
