Lensing by Kerr black holes
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Abstract
Interpreting horizon-scale observations of astrophysical black holes demands\na general understanding of null geodesics in the Kerr spacetime. These may be\ndivided into two classes: "direct" rays that primarily determine the\nobservational appearance of a given source, and highly bent rays that produce a\nnested sequence of exponentially demagnified images of the main emission: the\nso-called "photon ring". We develop heuristics that characterize the direct\nrays and study the highly bent geodesics analytically. We define three critical\nparameters $\\gamma$, $\\delta$, and $\\tau$ that respectively control the\ndemagnification, rotation, and time delay of successive images of the source,\nthereby providing an analytic theory of the photon ring. These observable\nparameters encode universal effects of general relativity, independent of the\ndetails of the emitting matter.\n