The two outer triangular caustics ( regions of infinite magnification ) of a close binary microlens move much faster than the components of the binary themselves , and can even exceed the speed of light .
When \epsilon \ga 1 , where \epsilon c is the caustic speed , the usual formalism for calculating the lens magnification breaks down .
We develop a new formalism that makes use of the gravitational analog of the Liénard-Wiechert potential .
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 \gg 1 .
Fourth , they grow weaker roughly in proportion to their increasing size .
Superluminal caustic-crossing events are probably not uncommon , but they are difficult to observe .