Black hole fusion in the extreme-mass-ratio limit

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. But no -- not always. In this work the student will see how the event horizon of the merger can be found in a simple way in the limit where one of the black holes is much smaller than the other, which is a situation that does occur in nature. Remarkably, the ideas and techniques involved are elementary: the equivalence principle, null geodesics in the Schwarzschild or Kerr solutions, and the notion of event horizon itself. The student will get a deeper appreciation of these notions, as well as develop some skills with Mathematica in the numerical solution of (simple) differential equations and in the graphic presentation of a realistic phenomenon that is happening right now in our Universe.