# Islands If one assumes complementarity, i.e., that the generalised entropy for the BH is the same as that of the radiation, then, given the Page curve for the former, we get Page curve for the latter for free. The island rule comes in when we want to drop this assumption and calculate the entropy of the radiation directly. Then one can do a replica calculation and find the island rule in the $n\to 1$ limit. ## Refs - original - [[2019#Almheiri, Mahajan, Maldacena, Zhao]] ## Comments Islands lie outside of stationary black holes and inside evaporating black holes (see [[2024#Matsuo]] for general proof). ## See also - root [[0131 Information paradox]] - [[0206 Replica wormholes]] ## Extended settings - non-evaporating setting: [[Urbach2019]][](https://arxiv.org/pdf/2105.15059.pdf) - [[0065 Defect CFT|ICFT]]: [[AnousMeineriPelliconiSonner2022]] - dCFT: [[HuLiMiao2022]][](https://arxiv.org/pdf/2208.11982.pdf) - transient islands: [[2021#Balasubramanian, Craps, Khramtsov, Shaghoulian]] - defect extremal surface: [[DengChuZhou2020]][](https://arxiv.org/pdf/2012.07612.pdf) - cosmology: [[Ben-DayanHadadWildenhain2022]][](https://arxiv.org/pdf/2211.16600.pdf) - warped black holes: [[2023#Anand]] ## Geometric conditions - [[BoussoShahbazi-Moghaddam2021]] - [[BoussoWildenhain2022]][](https://arxiv.org/pdf/2202.05278.pdf) ## Alternative understanding - from Hilbert space reduction: [[BasuWenZhou2022]][](https://arxiv.org/pdf/2211.17004.pdf)