In previous lectures, we formulated and resolved the naive information paradox. As a prelude to refining the information paradox, in this lecture we analysed the rate at which information must emerge from a black hole. This requires an assumption that is stronger than just unitarity. But, using insights from generic finite-dimensional systems in random states, we argued that the von Neumann entropy of the emitted Hawking radiation obeyed the "Page curve". This entropy increases monotonically until the black hole has lost about half its entropy, and then decreases monotonically down to zero when the black hole has evaporated completely. This will be an important ingredient in refined versions of the information paradox.

Lecture 19 notes