# Information paradox The black hole information paradox is the apparent inconsistency between the observations that the quantum state describing a young black hole is pure and that the thermal state describing the state of the universe after the black hole evaporates is mixed. More precisely, Hawking argued that the following three things cannot be all true: 1. finite BH entropy with state-counting interpretation; 2. unitary BH S-matrix; 3. EFT valid near/in the BH interior whenever there is a low curvature. ## Refs - reviews - [[2023#Harlow (Review)]] - pre-originals - [[2018#Almheiri]] - original (Page curve from [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]]) - [[2019#Almheiri, Engelhardt, Marolf, Maxfield]] - [[2019#Penington (May)]] - Page curve from [[0206 Replica wormholes|replica wormholes]] - "east coast": [[2019#Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini]] - "west coast": [[2019#Penington, Shenker, Stanford, Yang]] - [[0213 Islands|island]] formula - [[2019#Almheiri, Mahajan, Maldacena, Zhao]] - complementarity - [[2025#Engelhardt, Gesteau, Harlow]] \## Related - [[0007 RT surface]] - [[0212 Quantum extremal surface|QES]] - [[0216 Bra-ket wormholes]] - microscopic - [[Chakravarty2020]] - [[Reyes2021]][](https://arxiv.org/pdf/2103.01230.pdf) - direct calculation of entropy using a moving mirror - causality - [[2024#Concepcion, Nomura, Ritchie, Weiss]] ## Toy models - flat 2D - [[2020#Hartman, Shaghoulian, Strominger]] - good work for 2D, other two not so good (Chih-Hung) - [[2020#Anegawa, Iizuka]] - [[2020#Gautason, Schneiderbauer, Sybesma, Thorlacius]] - [[WangLiWang202104]][](https://arxiv.org/pdf/2104.00224.pdf) - AdS2 JT - [[GotoHartmanTajdini2020]][](https://arxiv.org/pdf/2011.09043.pdf) - recommended by Chih-Hung - [[2019#Almheiri, Engelhardt, Marolf, Maxfield]] - [[EngelsoyMertensVerlinde2016]] - [[2020#Hollowood, Kumar]] - 4D - [[WangLiWang2021]][](https://arxiv.org/pdf/2101.06867.pdf) (RN) - [[MedaPinaMontiRoncalloZanghi2021]][](https://arxiv.org/pdf/2103.02057.pdf) - spherical 4D BH using trace anomaly - reducing 3D to JT - [[VerheijdenVerlinde2021]][](https://arxiv.org/pdf/2102.00922.pdf) - QES from a higher dim RT/HRT - [[AlmheiriMahajanMaldacenaZhao2019]] - one-sided - [[GanDuShu2022]][](https://arxiv.org/pdf/2203.06310.pdf) - reducing 4D to 2D - [[DordevicGovaninGocaninRadovanovic2022]][](https://arxiv.org/pdf/2207.07409.pdf) - [[0181 AdS-BCFT|AdS/BCFT]] - [[2022#Kudler-Flam, Kusuki]] - non-gravitational models - [[2023#de Boer, Hollander, Rolph]]: a toy model of random dynamics - [[2024#Saha, Kulkarni, Dhar]]: a gas of non-interacting fermions on a lattice that is released from a box into the vacuum - [[0433 Membrane theory of entanglement dynamics|entanglement membrane]] - [[2024#Jiang, Blake, Thompson]] ## Reviews - [[AlmheiriHartmanMaldacenaShaghoulianTajdini2020]] - [[Raju2020]] ## Additional issues - add gravity to bath - [[GengKarchPerez-PardavilaRajuRandallRiojasShashi2020]] - soft hair issues - [[0214 Soft hairs as a resolution to information paradox]] - [[0195 Firewall]] - [[0187 Global symmetries in QG]] issues - unsorted - [[2020#Langhoff, Nomura]] ## Pure bulk studies - [[SchindlerFrangipaneAguirre2020]][](https://arxiv.org/abs/2012.07973) - using effective two-d theory [[BalbinotFabbri1999]] ## Quantum information issues - [[2020#Hayden, Penington]] - multipartite purification [[Bhattacharya2020]] - [[0204 Quantum complexity]] ## Concerns - [[Karlsson2021]][](https://arxiv.org/abs/2101.05879) ## Alternative diagnostics - [[2021#Kawabata, Nishioka, Okuyama, Watanabe (Feb)]] - capacity of entanglement - [[Patrascu2022]][](https://arxiv.org/pdf/2209.14709.pdf) - entanglement entropy not enough; need complexity ## Alternative understandings - Euclidean path integral with branching in Lorentzian evolution - [[ChenSasakiYeomYoon2021]][](https://arxiv.org/pdf/2111.01005.pdf) and [[ChenSasakiYeomYoon2022Essay]][](https://arxiv.org/abs/2205.08320) - [[Germani2022]][](https://arxiv.org/pdf/2204.13046.pdf) - no need for subdominant saddle - [[0415 Von Neumann algebra|vN algebraic]] - [[2024#Gomez]] ## Alternative proposals - [[Perry202106]][](https://arxiv.org/pdf/2106.03715.pdf) - [[Perry202108]][](https://arxiv.org/pdf/2108.05744.pdf) - free probabilistic: [[Wang2022]][](https://arxiv.org/pdf/2209.10546.pdf) ## Variants - de Sitter - [[GengNomuraSun2021]][](https://arxiv.org/pdf/2103.07477.pdf) - cost of curiosity - [[AalsmaSybesma2021]][](https://arxiv.org/pdf/2104.00006.pdf) - singularity forms if probing information inside BH - no page curve - [[Kames-KingVerheijdenVerlinde2021]][](https://arxiv.org/pdf/2108.09318.pdf) - gravitating baths - [[AndersonParrikarSoni2021]][](https://arxiv.org/abs/2103.14746) - multi-component CFT - [[2021#Fallows, Ross]] - disjoint regions - [[MiyataUgajin2021]] - very slow radiation - [[HollowoodKumarLegramandiTalwar2021]][](https://arxiv.org/pdf/2104.00052.pdf) - Dirichlet bath - [[GhoshKrisnan2021]][](https://arxiv.org/pdf/2103.17253.pdf) - [[0181 AdS-BCFT]] - [[ChuDengZhou2021]][](https://arxiv.org/pdf/2105.09106.pdf) - effective Hawking radiation - [[ChouLaoYang2021]][](https://arxiv.org/pdf/2111.14551.pdf) - finite temperature - [[VardhanKudler-FlamShapourianLiu2021]][](https://arxiv.org/abs/2112.00020) ## Extremal - [[KimNam2021]][](https://arxiv.org/pdf/2103.16163.pdf) ## Understanding - distinguishing random and BH microstates - [[Kudler-Flam2021]][](https://arxiv.org/abs/2102.05053) - [[Kudler-FlamNarovlanskyRyu202108]][](https://arxiv.org/pdf/2108.00011.pdf) ## Boundary understandings - Liouville theory [[HiranoKuroki2021]][](https://arxiv.org/pdf/2109.12539.pdf) ## Other quantities - [[0300 Mutual information|mutual information]]: - [[SahaGangopadhyaySaha2021]][](https://arxiv.org/pdf/2109.02996.pdf) - [[0264 Multi-partite entanglement|multi-partite entanglement]]: - [[2024#Iizuka, Lin, Nishida]]