A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Consider, in the domain of outer communication M+ of a Kerr-Newman black hole, a point p (observation event) and a timelike curve gamma (worldline of light source). Assume that gamma (i) has no past endpoint, (ii) does not intersect the caustic of the past light cone of p, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic lambda(k) of (Morse) index k from p to gamma, hence an observer at p sees infinitely many images of gamma. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in M+ are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman space-time the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal. (c) 2006 American Institute of Physics.