Spacetime diagrams are all well and good for standard static black holes.
You can fit the event horizon and the singularity in one picture with no problems. However, that is not so with charged and rotating black holes, for there are two event horizons to deal with, as well as the possiblity for recrossing those horizons. Roger Penrose developed a different kind of spacetime diagram for dealing with the more complex nature of the charged and rotating black holes. It would be good to start with something basic, and static black holes are as basic as you can get. Above are two diagrams of an eternal static black hole.