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We consider gravitational lensing of a background source by a finite system of point-masses. The problem of determining the maximum possible number of lensed images has been completely resolved in the single-plane setting (where the point masses all reside in a single lens plane), but this problem remains open in the multiplane setting. We construct examples of K-plane point-mass gravitational lens ensembles that produce ∏ i = 1 K (5 g i − 5) images of a single background source, where gi is the number of point masses in the ith plane. This gives asymptotically (for large gi with K fixed) 5K times the minimal number of lensed images. Our construction uses Rhie's single-plane examples and a structured parameter-rescaling algorithm to produce preliminary systems of equations with the desired number of solutions. Utilizing the stability principle from the differential topology, we then show that preliminary (nonphysical) examples can be perturbed to produce physically meaningful examples while preserving the number of solutions. We provide numerical simulations illustrating the result of our construction, including positions of lensed images and the structure of critical curves and caustics. We observe an interesting "caustic of multiplicity" phenomenon that occurs in the nonphysical case and has a noticeable effect on the caustic structure in the physically meaningful perturbative case. [ABSTRACT FROM AUTHOR]

In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr lensing to third order in our expansion parameter [variant_greek_epsilon], which is the ratio of the angular gravitational radius to the angular Einstein radius. We obtain new formulas and results for the bending angle, image positions, image magnifications, total unsigned magnification, and centroid, all to third order in [variant_greek_epsilon] and including the displacement. New results on the time delay between images are also given to second order in [variant_greek_epsilon], again including displacement. For all lensing observables we show that the displacement begins to appear only at second order in [variant_greek_epsilon]. When there is no spin, we obtain new results on the lensing observables for Schwarzschild lensing with displacement. [ABSTRACT FROM AUTHOR]

We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper, we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes that the source and observer are in the asymptotically flat region and does not require a small angle approximation. Furthermore, it takes into account the displacement that occurs when the light ray's tangent lines at the source and observer do not meet on the lens plane. We then explore our lens equation in the case when the compact object is a Kerr black hole. Specifically, we give an explicit expression for the displacement when the observer is in the equatorial plane of the Kerr black hole as well as for the case of spherical symmetry. [ABSTRACT FROM AUTHOR]