Retro-MACHOs: Pi in the sky?

Shine a flashlight on a black hole, and one is greeted with the return of a series of concentric rings of light. For a point source of light, and for perfect alignment of the lens, source, and observer, the rings are of infinite brightness (in the limit of geometric optics). In this manner, distant black holes can be revealed through their reflection of light from the Sun. Such retro-MACHO events involve photons leaving the Sun, making a Pi rotation about the black hole, and then returning to be detected at the Earth. Our calculations show that, although the light return is quite small, it may nonetheless be detectable for stellar-mass black holes at the edge of our solar system. For example, all (unobscured) black holes of mass M or greater will be observable to a limiting magnitude m, at a distance given by: 0.02 pc x \sqrt[3]{10^{(m-30)/2.5} (M/10 M_sun)^2}. Discovery of a Retro-MACHO offers a way to directly image the presence of a black hole, and would be a stunning confirmation of strong-field general relativity.