Extreme Gravitational Lensing near Rotating Black Holes

We describe a new approach to calculating photon trajectories and gravitational lensing effects in the strong gravitational field of the Kerr black hole. These techniques are applied to explore both the imaging and spectral properties of photons that perform multiple orbits of the central mass before escaping to infinity. Viewed at large inclinations, these higher order photons contribute $\sim 20 %$ of the total luminosity of the system for a Schwarzschild hole, whilst for an extreme Kerr black hole this fraction rises to $\sim 60 %$. In more realistic models these photons will be re-absorbed by the disc at large distances from the hole, but this returning radiation could provide a physical mechanism to resolve the discrepancy between the predicted and observed optical/UV colours in AGN. Conversely, at low inclinations, higher order images re-intercept the disc plane close to the black hole, so need not be absorbed by the disc if this is within the plunging region. These photons form a bright ring carrying approximately 10% of the total disc luminosity for a Schwarzchild black hole. The spatial separation between the inner edge of the disc and the ring is similar to the size of the event horizon. This is resolvable for supermassive black holes with proposed X-ray interferometery missions such as MAXIM, so has the potential to provide an observational test of strong field gravity.