Suppose we are given a globally hyperbolic spacetime (M,g) solving the Einstein vacuum equations, and a timelike geodesic in M. I will explain how to construct, on any compact subset of M, a solution g_\epsilon of the Einstein vacuum equations which is approximately equal to g far from the geodesic but near any point along the geodesic approximately equal to the metric of a Kerr black hole with mass \epsilon. As an application, we can construct spacetimes which describe the merger of a very light black hole with a unit mass black hole, followed by the relaxation of the resulting single black hole to its equilibrium (Kerr or Kerr-de Sitter) state. In the geometry seminar, I will focus on the more geometric aspects of the problem, while in the analysis seminar on the same topic I will discuss some of the underlying estimates for waves on families of spacetimes degenerating in this particular fashion.