A Kerr black hole with mass parameter m and angular momentum parameter a
acting as a gravitational lens gives rise to two images in the weak field
limit. We study the corresponding magnification relations, namely the signed
and absolute magnification sums and the centroid up to post-Newtonian order. We
show that there are post-Newtonian corrections to the total absolute
magnification and centroid proportional to a/m, which is in contrast to the
spherically symmetric case where such corrections vanish. Hence we also propose
a new set of lensing observables for the two images involving these
corrections, which should allow measuring a/m with gravitational lensing. In
fact, the resolution capabilities needed to observe this for the Galactic black
hole should in principle be accessible to current and near-future
instrumentation. Since a/m >1 indicates a naked singularity, a most interesting
application would be a test of the Cosmic Censorship conjecture. The technique
used to derive the image properties is based on the degeneracy of the Kerr lens
and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple
physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in
Phys. Rev.
