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Fractal structures in the deflection of light by a pair of Schwarzschild black holes

The deflection of light by the strong gravitational field produced by a pair of supermassive Schwarzschild black holes is considered from the point of view of an open conservative nonlinear dynamical system. From an approximate solution of the geodesic equation we obtained a two-dimensional map describing the impact parameter and scattering angle just before the light deflection by each black hole. Since the system is typically non-integrable, there is a parameter range for which chaotic area-filling orbits occur. The dynamics underlying those chaotic orbits involves a number of fractal structures related to the existence of a non-attractive invariant chaotic set. The outcome of a typical light ray approaching the system can be either diverged to infinity or falling into one of the black holes. Non-typical light rays can orbit around the black hole pair as periodic orbits. We identified the corresponding escape basins and their fractal boundaries, using two approaches: the computation of the uncertainty exponents and the corresponding basin and basin boundary entropies. We also exhibited the so-called Wada property showing qualitative pieces of evidence of this property.