Black hole fusion made easy

The fusion of two black holes - a signature phenomenon of General Relativity is usually regarded as a process so complex that nothing short of a supercomputer simulation can accurately capture it. In this essay, we explain how the event horizon of the merger can be found in an exact analytic way in the limit where one of the black holes is much smaller than the other. Remarkably, the ideas and techniques involved are elementary: the equivalence principle, null geodesics in the Schwarzschild solution, and the notion of event horizon itself. With these, one can identify features such as the line of caustics at which light rays enter the horizon, and find indications of universal critical behavior when the two black holes touch.