{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T02:25:39Z","timestamp":1775960739597,"version":"3.50.1"},"reference-count":61,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,12,30]],"date-time":"2016-12-30T00:00:00Z","timestamp":1483056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element\u2014forming of the event horizon before the evaporation begins\u2014is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.<\/jats:p>","DOI":"10.3390\/e19010017","type":"journal-article","created":{"date-parts":[[2016,12,30]],"date-time":"2016-12-30T08:48:53Z","timestamp":1483087733000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The Information Recovery Problem"],"prefix":"10.3390","volume":"19","author":[{"given":"Valentina","family":"Baccetti","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viqar","family":"Husain","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Terno","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/248030a0","article-title":"Black hole explosions?","volume":"248","author":"Hawking","year":"1974","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1103\/PhysRevD.14.2460","article-title":"Breakdown of predictability in gravitational collapse","volume":"14","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/0370-1573(95)00008-5","article-title":"A primer for black hole quantum physics","volume":"260","author":"Brout","year":"1995","journal-title":"Phys. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Frolov, V., and Novikov, I. (1998). Black Hole Physics: Basic Concepts and New Developments, Kluwer.","DOI":"10.1007\/978-94-011-5139-9"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wald, R.M. (2001). The Thermodynamics of Black Holes. Living Rev. Relativ., 4.","DOI":"10.12942\/lrr-2001-6"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Mann, R.B. (2015). Black Holes: Thermodynamics, Information, and Firewalls, Springer.","DOI":"10.1007\/978-3-319-14496-2"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"015002","DOI":"10.1103\/RevModPhys.88.015002","article-title":"Jerusalem lectures on black holes and quantum information","volume":"88","author":"Harlow","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bru\u00df, D., and Leuchs, G. (2007). Lectures on Quantum Information, Wiley-VCH.","DOI":"10.1002\/9783527618637"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wilde, M.W. (2013). Quantum Information Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139525343"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1103\/RevModPhys.76.93","article-title":"Quantum information and relativity theory","volume":"76","author":"Peres","year":"2004","journal-title":"Rev. Mod. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Mann, R.B., and Ralph, T.C. (2012). Relativistic quantum information. Class. Quant. Grav., 29.","DOI":"10.1088\/0264-9381\/29\/22\/220301"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1103\/RevModPhys.81.865","article-title":"Quantum entanglement","volume":"81","author":"Horodecki","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1103\/PhysRevA.59.3320","article-title":"Nonlinear operations in quantum-information theory","volume":"59","author":"Terno","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3743","DOI":"10.1103\/PhysRevD.48.3743","article-title":"The stretched horizon and black hole complementarity","volume":"48","author":"Susskind","year":"1993","journal-title":"Phys. Rev. D"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Almhieri, A., Marolf, D., Polchinski, J., and Sully, J. (2013). Black Holes: Complementarity or Firewalls?. J. High Energy Phys., 2013.","DOI":"10.1007\/JHEP02(2013)062"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"101301","DOI":"10.1103\/PhysRevLett.110.101301","article-title":"Better Late than Never: Information Retrieval from Black Holes","volume":"110","author":"Braunstein","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bryan, K.L.H., and Medved, A.J.M. (2016). Black holes and information: A new take on an old paradox. arXiv.","DOI":"10.1155\/2017\/7578462"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4341","DOI":"10.1103\/PhysRevA.60.4341","article-title":"Sufficient conditions for a disentanglement","volume":"60","author":"Mor","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"15007","DOI":"10.1038\/npjqi.2015.7","article-title":"Replicating the benefits of Deutschian closed timelike curves without breaking causality","volume":"1","author":"Yuan","year":"2015","journal-title":"NPJ Quantum Inf."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Louko, J. (2014). Unruh-DeWitt detector response across a Rindler firewall is finite. J. High Energy Phys., 2014.","DOI":"10.1007\/JHEP09(2014)142"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1002\/prop.201300020","article-title":"Cool horizons for entangled black holes","volume":"61","author":"Maldacena","year":"2013","journal-title":"Fortschr. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1103\/PhysRevLett.75.1872","article-title":"Topological Censorship","volume":"75","author":"Friedman","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1103\/PhysRev.118.1110","article-title":"Wormhole Initial Conditions","volume":"118","author":"Misner","year":"1960","journal-title":"Phys. Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/S0375-9601(02)01806-6","article-title":"Localization and causality for a free particle","volume":"308","author":"Barat","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"042111","DOI":"10.1103\/PhysRevA.89.042111","article-title":"Localization of relativistic particles and uncertainty relations","volume":"89","author":"Terno","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Horowitz, G.T., and Maldacena, J.M. (2004). The black hole final state. J. High Energy Phys., 2004.","DOI":"10.1088\/1126-6708\/2004\/02\/008"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lloyd, S., and Preskill, J. (2014). Unitarity of black hole evaporation in final-state projection models. J. High Energy Phys., 2014.","DOI":"10.1007\/JHEP08(2014)126"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"040403","DOI":"10.1103\/PhysRevLett.106.040403","article-title":"Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency","volume":"106","author":"Lloyd","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Baez, J.C., and Vicary, J. (2014). Wormholes and entanglement. Class. Quantum Grav., 31.","DOI":"10.1088\/0264-9381\/31\/21\/214007"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5042","DOI":"10.1103\/PhysRevLett.85.5042","article-title":"Hawking Radiation as Tunneling","volume":"85","author":"Parikh","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Singleton, D., Vagenas, E.C., Zhu, T., and Ren, J.R. (2010). Insights and possible resolution to the information loss paradox via the tunneling picture. J. High Energy Phys., 2010.","DOI":"10.1007\/JHEP08(2010)089"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"071302","DOI":"10.1103\/PhysRevLett.107.071302","article-title":"Black Hole Evaporation Rates without Spacetime","volume":"107","author":"Braunstein","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.aop.2010.11.015","article-title":"Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox","volume":"326","author":"Zhang","year":"2011","journal-title":"Ann. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1341014","DOI":"10.1142\/S0218271813410149","article-title":"Information conservation is fundamental: Recovering the lost information in hawking radiation","volume":"22","author":"Zhang","year":"2013","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1103\/PhysRevD.14.1479","article-title":"The mechanism of blackbody radiation from an incipient black hole","volume":"14","author":"Gerlach","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"104012","DOI":"10.1103\/PhysRevD.64.104012","article-title":"Gravitational collapse of a radiating shell","volume":"64","author":"Alberghi","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Barcel\u00f3, C., Liberati, S., Sonego, S., and Visser, M. (2006). Quasi-particle creation by analogue black holes. Class. Quantum Grav., 23.","DOI":"10.1088\/0264-9381\/23\/17\/014"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"044032","DOI":"10.1103\/PhysRevD.77.044032","article-title":"Fate of gravitational collapse in semiclassical gravity","volume":"77","author":"Liberati","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"024005","DOI":"10.1103\/PhysRevD.76.024005","article-title":"Observation of incipient black holes and the information loss problem","volume":"76","author":"Vachaspati","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1350050","DOI":"10.1142\/S0217751X13500504","article-title":"A self-consistent model of the black hole evaporation","volume":"28","author":"Kawai","year":"2013","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_41","unstructured":"Poisson, E. (2004). A Relativist\u2019s Toolkit, Cambridge University Press."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.physletb.2015.12.076","article-title":"Hawking radiation, the Stefan\u2013Boltzmann law, and unitarization","volume":"754","author":"Giddings","year":"2016","journal-title":"Phys. Lett. B"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2720","DOI":"10.1103\/PhysRevD.13.2720","article-title":"Energy-momentum tensor near an evaporating black hole","volume":"13","author":"Davies","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"111301","DOI":"10.1103\/PhysRevLett.114.111301","article-title":"Radiation from a Collapsing Object is Manifestly Unitary","volume":"114","author":"Saini","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1103\/PhysRev.83.10","article-title":"Nonstatic Solutions of Einstein\u2019s Field Equations for Spheres of Fluids Radiating Energy","volume":"83","author":"Vaidya","year":"1951","journal-title":"Phys. Rev."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/S0370-2693(99)00071-4","article-title":"Global structure of evaporating black holes","volume":"449","author":"Parikh","year":"1999","journal-title":"Phys. Lett. B"},{"key":"ref_47","unstructured":"Baccetti, V., Mann, R.B., and Terno, D.R. (2016). Role of evaporation in gravitational collapse. arXiv."},{"key":"ref_48","unstructured":"Kay, B.S. (1998). Entropy efined, Entropy Increase and Decoherence Understood, and Some Black-Hole Puzzles Solved. arXiv."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Kay, B.S. (1998). Decoherence of macroscopic closed systems within Newtonian quantum gravity. Class. Quantum Grav., 15.","DOI":"10.1088\/0264-9381\/15\/12\/003"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1103\/PhysRevLett.70.9","article-title":"Universality and scaling in gravitational collapse of a massless scalar field","volume":"70","author":"Choptuik","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"104001","DOI":"10.1103\/PhysRevD.71.104001","article-title":"Flat slice Hamiltonian formalism for dynamical black holes","volume":"71","author":"Husain","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"044039","DOI":"10.1103\/PhysRevD.81.044039","article-title":"Dynamics and entanglement in spherically symmetric quantum gravity","volume":"81","author":"Husain","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"042113","DOI":"10.1103\/PhysRevA.77.042113","article-title":"Dynamics beyond completely positive maps: Some properties and applications","volume":"77","author":"Carteret","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1002\/prop.201300037","article-title":"Origin of the blackhole information paradox","volume":"62","author":"Brustein","year":"2014","journal-title":"Fortschr. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Abramowicz, M.A., and Fragile, P.C. (2013). Foundations of Black Hole Accretion Disk Theory. Living Rev. Relativ., 16.","DOI":"10.12942\/lrr-2013-1"},{"key":"ref_56","unstructured":"LIGO Scientific Collaboration and Virgo Collaboration (2016). Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett., 116, 061102."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"8174","DOI":"10.3390\/e17127873","article-title":"Entropy and Quantum Gravity","volume":"17","author":"Kay","year":"2015","journal-title":"Entropy"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"151102","DOI":"10.1103\/PhysRevLett.114.151102","article-title":"No-Hair Theorem for Black Holes in Astrophysical Environments","volume":"114","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"231301","DOI":"10.1103\/PhysRevLett.116.231301","article-title":"Soft Hair on Black Holes","volume":"116","author":"Hawking","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1007\/s10701-007-9144-6","article-title":"Relational Physics with Real Rods and Clocks and the Measurement Problem of Quantum Mechanics","volume":"37","author":"Gambini","year":"2007","journal-title":"Found. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"080401","DOI":"10.1103\/PhysRevLett.103.080401","article-title":"Quantum Solution to the Arrow-of-Time Dilemma","volume":"103","author":"Maccone","year":"2009","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/1\/17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:29:36Z","timestamp":1760210976000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/1\/17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,30]]},"references-count":61,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["e19010017"],"URL":"https:\/\/doi.org\/10.3390\/e19010017","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,30]]}}}