Superluminal caustics of close, rapidly rotating binary microlenses

The two outer triangular caustics (regions of infinite magnification) of a close binary microlens move much faster than the components of the binary t hemselves, and can even exceed the speed of light. When epsilon greater tha n or similar to 1, where epsilon c is the caustic speed, the usual formalis m for calculating the lens magnification breaks dow. We develop a new forma lism that makes use of the gravitational analog of the Lienard-Wiechert pot ential. We find that as the binary speeds up, the caustics undergo several related changes: First, their position in space drifts. Second, they rotate about their own axes so that they no longer have a cusp facing the binary center of mass. Third, they grow larger and dramatically so for epsilon muc h greater than 1. Fourth, they grow weaker roughly in proportion to their i ncreasing size. Superluminal caustic-crossing events are probably not uncom mon, but they are difficult to observe.