Lecture 13: The Area theorem
In the previous lecture, we derived the main technical input required for the myriad global theorems about black holes---the Raychaudhuri equation. The area theorem follows from simple reasoning about horizons and the application of this equation. First, we show that the horizon is generated by null geodesics that do not intersect. Then it follows that the expansion at each point must be positive, unless the horizon itself hits a singularity. Assuming that this does not happen, the area of the horizon must increase along its future-directed null coordinate.
