Ingemar Bengtsson: Limits of spacetimes, revisited

Given a one-parameter family of spacetimes, say Reissner-Nordström as a function of charge, there may be several ways of taking limits, say the limit where charge equals mass. Depending on how the limit is taken, very different regions of the original spacetime survive in the limit. All this was clarified by Geroch long ago. I will explain his explanation by means of a metrically correct version of the Penrose diagrams, so that we can actually see the different ways in which spacetime is deformed by the limiting process.