On Strong Gravitational Lensing in Rotating Galactic Space-times

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.