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

Abstract

The deflection of light by a pair of black holes can be considered an open conservative non-linear dynamic system. The basis of our approach is our understanding of strong gravitational lensing and the geodesic movement of light. We obtain a two-dimensional map that sets out the impact parameter and the escape angle when the light gets deflected by each black hole. Being a non-integrable system, the chaotic area-filling orbits occur in a specific parameter range. Fractal structures are related to the existence of a non-attractive invariant chaotic set. This can be seen in the dynamics of these chaotic orbits. The light-ray that enters the system has two potential defined outcomes. Either the light ray can diverge to infinity or it will fall into one of the two black holes. We describe the escape basins and their boundaries, adopting two methods: firstly the corresponding basin and basin boundary entropies and secondly the computation of the uncertainty exponents.