Evaporating black holes lose complexity after the Page time

Using a two-dimensional gravity model with an end-of-the-world brane to mimic Hawking evaporation, the authors track how the complexity of the black hole interior evolves over time. Unlike static black holes — where complexity grows linearly for an exponentially long time before plateauing — the evaporating case peaks at the Page time and then decays exponentially. Beyond the Page time, fluctuations around the average grow large, signaling a breakdown of self-averaging: the ensemble mean is dominated by rare, atypical configurations rather than generic ones. The result suggests that evaporation fundamentally restructures the interior geometry in ways not captured by non-evaporating models.