In Lecture 3, we considered the causal structure of the R-N black hole. At first sight, this leads to an exotic Penrose diagram. But after we looked at this diagram more closely and considered the instability of the inner horizon, the conclusion was that, qualitatively, for realistic collapse leading to a charged black hole or a charged rotating black hole, the causal structure of the spacetime is much like the causal structure of the Oppenheimer-Snyder solution.
We also considered the causal structure of the AdS black hole, which is much like the usual Schwarzschild black hole, except that it has a boundary.
Finally, we started to consider the Penrose process, which will serve as an entry-point into black hole thermodynamics.