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Full list of authors: Amaro-Seoane, Pau; Andrews, Jeff; Sedda, Manuel Arca; Askar, Abbas.; Baghi, Quentin; Balasov, Razvan; Bartos, Imre; Bavera, Simone S.; Bellovary, Jillian; Berry, Christopher P. L.; Berti, Emanuele; Bianchi, Stefano; Blecha, Laura; Blondin, Stephane; Bogdanovic, Tamara; Boissier, Samuel; Bonetti, Matteo; Bonoli, Silvia; Bortolas, Elisa; Breivik, Katelyn; Capelo, Pedro R.; Caramete, Laurentiu; Cattorini, Federico; Charisi, Maria; Chaty, Sylvain; Chen, Xian; Chruslinska, Martyna; Chua, Alvin J. K.; Church, Ross; Colpi, Monica; D'Orazio, Daniel; Danielski, Camilla; Davies, Melvyn B.; Dayal, Pratika; De Rosa, Alessandra; Derdzinski, Andrea; Destounis, Kyriakos; Dotti, Massimo; Dutan, Ioana; Dvorkin, Irina; Fabj, Gaia; Foglizzo, Thierry; Ford, Saavik; Fouvry, Jean-Baptiste; Franchini, Alessia; Fragos, Tassos; Fryer, Chris; Gaspari, Massimo; Gerosa, Davide; Graziani, Luca; Groot, Paul; Habouzit, Melanie; Haggard, Daryl; Haiman, Zoltan; Han, Wen-Biao; Istrate, Alina; Johansson, Peter H.; Khan, Fazeel Mahmood; Kimpson, Tomas; Kokkotas, Kostas; Kong, Albert; Korol, Valeriya; Kremer, Kyle; Kupfer, Thomas; Lamberts, Astrid; Larson, Shane; Lau, Mike; Liu, Dongliang; Lloyd-Ronning, Nicole; Lodato, Giuseppe; Lupi, Alessandro; Ma, Chung-Pei; Maccarone, Tomas; Mandel, Ilya; Mangiagli, Alberto; Mapelli, Michela; Mathis, Stephane; Mayer, Lucio; McGee, Sean; McKernan, Berry; Miller, M. Coleman; Mota, David F.; Mumpower, Matthew; Nasim, Syeda S.; Nelemans, Gijs; Noble, Scott; Pacucci, Fabio; Panessa, Francesca; Paschalidis, Vasileios; Pfister, Hugo; Porquet, Delphine; Quenby, John; Ricarte, Angelo; Roepke, Friedrich K.; Regan, John; Rosswog, Stephan; Ruiter, Ashley; Ruiz, Milton; Runnoe, Jessie; Schneider, Raffaella; Schnittman, Jeremy; Secunda, Amy; Sesana, Alberto; Seto, Naoki; Shao, Lijing; Shapiro, Stuart; Sopuerta, Carlos; Stone, Nicholas C.; Suvorov, Arthur; Tamanini, Nicola; Tamfal, Tomas; Tauris, Thomas; Temmink, Karel; Tomsick, John; Toonen, Silvia; Torres-Orjuela, Alejandro; Toscani, Martina; Tsokaros, Antonios; Unal, Caner; Vazquez-Aceves, Veronica; Valiante, Rosa; van Putten, Maurice; van Roestel, Jan; Vignali, Christian; Volonteri, Marta; Wu, Kinwah; Younsi, Ziri; Yu, Shenghua; Zane, Silvia; Zwick, Lorenz; Antonini, Fabio; Baibhav, Vishal; Barausse, Enrico; Bonilla Rivera, Alexander; Branchesi, Marica; Branduardi-Raymont, Graziella; Burdge, Kevin; Chakraborty, Srija; Cuadra, Jorge; Dage, Kristen; Davis, Benjamin; de Mink, Selma E.; Decarli, Roberto; Doneva, Daniela; Escoffier, Stephanie; Gandhi, Poshak; Haardt, Francesco; Lousto, Carlos O.; Nissanke, Samaya; Nordhaus, Jason; O'Shaughnessy, Richard; Portegies Zwart, Simon; Pound, Adam; Schussler, Fabian; Sergijenko, Olga; Spallicci, Alessandro; Vernieri, Daniele; Vigna-Gomez, Alejandro.-- This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/., The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA’s first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultra-compact stellar-mass binaries, massive black hole binaries, and extreme or interme-diate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe. © The Author(s) 2023, corrected publication 2023., P. Dayal acknowledges support from the European Research council (ERC-717001) and from the Netherlands Research Council NWO (016.VIDI.189.162). P.H. Johansson acknowledges the support from the European Research Council (ERC-818930). S. Toonen acknowledges support from the Netherlands Research Council NWO (VENI 639.041.645 Grants) C. Unal is supported by European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (Project CoGraDS - CZ.02.1.01/0.0/0.0/15_003/0000437). S. Chaty acknowledges the LabEx UnivEarthS for the funding of Interface project I10 “From binary evolution towards merging of compact objects”. A. De Rosa acknowledges financial contribution from the agreement ASI-INAF n.2017-14-H.O E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Gerosa is supported by European Union’s H2020 ERC Starting Grant No. 945155–GWmining, Leverhulme Trust Grant No. RPG-2019-350 and Royal Society Grant No. RGS-R2-202004. T. Bogdanovic acknowledges support by the NASA award No. 80NSSC19K0319 and by the NSF award AST-1908042. D. Porquet acknowledges funding support from CNES. C. Danielski acknowledges financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) B.L. Davis acknowledges support from Tamkeen under the NYU Abu Dhabi Research Institute Grant CAP3. F. Pacucci acknowledges support from a Clay Fellowship by the SAO and from the Black Hole Initiative, which is funded by grants from the John Templeton Foundation and the Gordon and Betty Moore Foundation. A.J. Ruiter acknowledges support from the Australian Research Council Future Fellowship Grant FT170100243. V. Paschalidis is supported by NSF Grant PHY-1912619 and NASA Grant 80NSSC20K1542 to the University of Arizona, and NSF-XSEDE Grant TG-PHY190020. D. Haggard acknowledges support from the NSERC Discovery Grant and Canada Research Chairs programs, and the Bob Wares Science Innovation Prospectors Fund. M. Toscani acknowledges European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 823823 (RISE DUSTBUSTERS project) and COST Action CA16104 - Gravitational waves, black holes and fundamental physics, supported by COST (European Cooperation in Science and Technology). M. Chruslinska, A. Istrate and G. Nelemans acknowledge support from Netherlands Research Council NWO. T. Fragos and S. Bavera acknowledge support from a Swiss National Science Foundation Professorship Grant (project numbers PP00P2_176868 and PP00P2_211006)., With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2021-001131-S).

et al., The science objectives of the LISA mission have been defined under the implicit assumption of a 4-years continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of ≈0.75 , which would reduce the effective span of usable data to 3 years. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 years of mission operations is recommended., C.P.L. Berry is supported by the CIERA Board of Visitors Professorship. E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Blas acknowledges support from the Fundación Jesus Serra and the Instituto de Astrofísica de Canarias under the Visiting Researcher Programme 2021 agreed between both institutions. T. Bogdanović acknowledges the support by the National Aeronautics and Space Administration (NASA) under award No. 80NSSC19K0319 and by the National Science Foundation (NSF) under Award No. 1908042. V. Cardoso acknowledges financial support provided under the European Union’s H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” Grant Agreement No. MaGRaTh–646597. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101007855. We thank FCT for financial support through Projects No. UIDB/00099/2020 and through grants PTDC/MAT-APL/30043/2017 and PTDC/FIS-AST/7002/2020. H.-Y. Chen is supported by NASA through NASA Hubble Fellowship Grants No. HST-HF2-51452.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. Z. Haiman acknowledges support by NASA Grant NNX15AB19G and NSF Grants AST-2006176 and AST-1715661. G. Nardini is partly supported by the ROMFORSK Grant Project. No. 302640 “Gravitational Wave Signals From Early Universe Phase Transitions”. P. Pani acknowledges financial support provided under the European Union’s H2020 ERC, Starting Grant Agreement No. DarkGRA–757480. He also acknowledges support under the MIUR PRIN and FARE programmes (GW-NEXT, CUP: B84I20000100001), and by the Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001). A. Sesana acknowledges financial support provided under the European Union’s H2020 ERC Consolidator Grant “Binary Massive Black Hole Astrophysics” (B Massive, Grant Agreement: 818691). K. Yagi acknowledges support from NSF Grant PHY-1806776, NASA Grant 80NSSC20K0523, a Sloan Foundation Research Fellowship and the Owens Family Foundation. D. J. Weir was supported by a Science and Technology Facilities Council Ernest Rutherford Fellowship, Grant no. ST/R003904/1, and by the Academy of Finland, Grants 324882 and 328958. A. Zimmerman is supported by NSF Grant No. PHY-1912578. The authors would like to acknowledge networking support by the GWverse COST Action CA16104, “Black holes, gravitational waves and fundamental physics.” The Flatiron Institute is supported by the Simons Foundation. This research has made use of data, software and web tools obtained from the Gravitational Wave Open Science Center (www.gw-openscience.org/), a service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo Collaboration. LIGO Laboratory and Advanced LIGO are funded by the United States National Science Foundation (NSF) as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain.

69 pages, 21 figures. Accepted for publication in New Astronomy Reviews © 2020 Elsevier B.V., The quest for binary and dual supermassive black holes (SMBHs) at the dawn of the multi-messenger era is compelling. Detecting dual active galactic nuclei (AGN) -- active SMBHs at projected separations larger than several parsecs -- and binary AGN -- probing the scale where SMBHs are bound in a Keplerian binary -- is an observational challenge. The study of AGN pairs (either dual or binary) also represents an overarching theoretical problem in cosmology and astrophysics. The AGN triggering calls for detailed knowledge of the hydrodynamical conditions of gas in the imminent surroundings of the SMBHs and, at the same time, their duality calls for detailed knowledge on how galaxies assemble through major and minor mergers and grow fed by matter along the filaments of the cosmic web. This review describes the techniques used across the electromagnetic spectrum to detect dual and binary AGN candidates and proposes new avenues for their search. The current observational status is compared with the state-of-the-art numerical simulations and models for formation of dual and binary AGN. Binary SMBHs are among the loudest sources of gravitational waves (GWs) in the Universe. The search for a background of GWs at nHz frequencies from inspiralling SMBHs at low redshifts, and the direct detection of signals from their coalescence by the Laser Interferometer Space Antenna in the next decade, make this a theme of major interest for multi-messenger astrophysics. This review discusses the future facilities and observational strategies that are likely to significantly advance this fascinating field.© 2020 Elsevier B.V., All authors acknowledge the hospitality of the Lorentz Center for international workshops (Leiden, The Netherlands), where the idea of this work was born, and acknowledge the support of the International Space Science Institute (ISSI Bern, Switzerland), where the collaboration was originated. We thank the reviewers for having provided valuable and constructive comments that improved the clarity of the manuscript, and J.E. Barnes, L. Blecha, M. Eracleous, B.D. Farris, H. Fu, X. Liu, R. Pfeifle, L.C. Popovic, C. Ricci, S. Rodriguez, S. Tang, G. B. Taylor for their kind permission to reuse figures from their publications. ADR, CV and SB acknowledge financial support from ASI under grant ASI-INAF I/037/12/0 , and from the agreement ASI-INAF n. 2017-14-H.O . TB acknowledges support by the National Aeronautics and Space Administration under Grant No. NNX15AK84G and 80NSSC19K0319 issued through the Astrophysics Theory Program and by the Research Corporation for Science Advancement through a Cottrell Scholar Award. SF and KÉG thank the Hungarian National Research, Development, and Innovation Office ( OTKA NN110333 ) for support. KÉG was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP-19-4 New National Excellence Program of the Ministry for Innovation and Technology. BH acknowledges financial support by the DFG grant GE625/17-1 . EL is supported by a European Union COFUND/Durham Junior Research Fellowship (under EU grant agreement no. 609412). DL acknowledges support from the European Research Council (ERC) under grant 647208 (PI Jonker). AS is supported by the ERC CoG grant 818691 (B Massive). MGi is supported by the “Programa de Atracción de Talento” of the Comunidad de Madrid grant 2018-T1/TIC-11733 for the project: “Unveiling Black Hole Winds from Space”, and by the Spanish State Research Agency (AEI) grant MDM-2017-0737 Unidad de Excelencia “María de Maeztu” - Centro de Astrobiología (INTA-CSIC). PRC and LM acknowledge support from the Swiss National Science Foundation under the Grant 200020_178949 . MC acknowledges support from the National Science Foundation (NSF) NANOGrav Physics Frontier Center, award number 1430284 . NHR acknowledges support from the BMBF Verbundforschung under FKZ: 05A17PC1 and FKZ: 05A17PC2. ZH acknowledges support from NASA grants NNX17AL82G and 80NSSC19K0149 and NSF grant 1715661 . KI acknowledges support by the Spanish MINECO under grant AYA2016-76012-C3-1-P and MDM-2014-0369 of ICCUB (Unidad de Excelencia ’María de Maeztu’). MPT acknowledges financial support from the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía ( SEV-2017-0709 ) and through the MINECO grants AYA2012-38491-C02-02 and AYA2015-63939-C2-1-P .