I will discuss recent work that studies the evolution of the von Neumann entropy of a holographic boundary system dual to an evaporating black hole in AdS. This entropy is computed via the Engelhardt-Wall prescription of extremizing the generalized entropy functional, which is given by the sum of the area of a surface homologous to the boundary and the entropy of bulk matter on any spacelike region bounded by this homologous surface and the boundary. I'll present the surprising result of how this prescription, applied purely within the semiclassical approximation, correctly reproduces expected features of unitary black hole evaporation, such as the Page curve. I'll also discuss how the Hayden-Preskill protocol is realized, and share some thoughts on possible resolutions of the information and firewall paradoxes.

Refs:

Section 4.3 of https://arxiv.org/abs/1810.02055

https://arxiv.org/abs/1905.08762

https://arxiv.org/abs/1905.08255