  We study the motion of light in the gravitational field of two Schwarzschild
black holes, making the approximation that they are far apart, so that the
motion of light rays in the neighborhood of one black hole can be considered to
be the result of the action of each black hole separately. Using this
approximation, the dynamics is reduced to a 2-dimensional map, which we study
both numerically and analytically. The map is found to be chaotic, with a
fractal basin boundary separating the possible outcomes of the orbits (escape
or falling into one of the black holes). In the limit of large separation
distances, the basin boundary becomes a self-similar Cantor set, and we find
that the box-counting dimension decays slowly with the separation distance,
following a logarithmic decay law.
