Scattering map for two black holes

We study the motion of light in the gravitational field of two Schwarzschil d black holes, making the approximation that they are far apart, so that th e motion of light rays in the neighborhood of one black hole can be conside red to be the result of the action of each black hole separately. Usings th is approximation, the dynamics is reduced to a two-dimensional map, which w e study both numerically and analytically. The map is found to be chaotic, with a fractal basin boundary separating the possible outcomes of the orbit s (escape or falling into one of the black holes). In the limit of large se paration distances, the basin boundary becomes a self-similar Canter set, a nd we find that the box-counting dimension decays slowly with the separatio n distance, following a logarithmic decay law.