collapse of massive stars and supermassive stars to a stellar-mass and supermassive
black hole [1982], to the post-merger evolution of the neutron-star binaries [1983],
and to collapsar modeling [1984].

**SpEC** The Spectral Einstein Code (SpEC) [674] is a pseudo-spectral GR code developed by the Simulating eXtreme Spacetimes collaboration. SpEC is capable of evolving BBH and binaries with neutron stars. It incorporates an elliptic solver to construct initial data [530, 534, 537], eccentricity reduction [1985–1987], constraint-preserving and non-reflective outer boundary conditions [544, 1988, 1989], and implements hp-AMR [744, 1990]. Extracted gravitational waves are extrapolated to future null infinity [523, 556, 1991] and corrected for center-of-mass drift [1992]. SpEC is a highly accurate NR code for BBH, and has computed large waveform catalogs of BBH inspirals encompassing several tens of orbits [521, 523]. SpEC has evolved BBH with spins as large as 0.994 [1993], inspirals as long as 170 orbits [584] as well as eccentric binaries [717].

**SpECTRE** The Simulating eXtreme Spacetimes collaboration is developing the next-
generation code SpECTRE [676, 677], which uses a discontinuous-Galerkin-
finite-difference hybrid method [1994–1996] for accurate and robust neutron star
simulations combined with task-based parallelism, showing good scaling to over
600,000 cores [676]. Using Cauchy-Characteristic extraction, SpECTRE is able
to resolve gravitational wave memory [560, 561] and improve hybridization with
post-Newtonian waveforms by ensuring numerical relativity waveforms are in the
same BMS frame as the post-Newtonian waveforms [563]. Improvements for
efficiently simulating binary black holes with mass ratios $q > 10$ aim to reduce
the computational cost of such simulations by a factor of $q$ [695]. SpECTRE also
incorporates a flexible elliptic solver [541, 1997, 1998].

**Spritz** Spritz is an open-source code that solves the equations of general relativistic magnetohydrodynamics and that can take into account finite temperature nuclear equations of state and neutrino emission [643, 1999, 2000]. The code is based on the Einstein Toolkit framework and implements also high-order methods for the hydrodynamic equations.

**WhiskyMHD** WhiskyMHD is a fully general relativistic magnetohydrodynamic code based on the Einstein Toolkit [648]. The code has been used mainly to perform simulations of binary neutron star mergers, but it has also been used to perform the first simulations of magnetized plasma around merging supermassive black holes in the ideal magnetohydrodynamic approximation [2001].

## Acknowledgements

We would like to thank our internal reviewers, Leor Barack, Christopher Berry, and Nelson Christensen for extremely helpful feedback. Sarp Akçay acknowledges University College Dublin's Ad Astra Fund. Pau Amaro Seoane acknowledges the
funds from the "European Union NextGenerationEU/PRTR", Programa de Planes Complementarios I+D+I (ref. ASFAE/2022/014). Enrico Barausse acknowledges support from the European Union's H2020 ERC Consolidator Grant "GRavity from Astrophysical to Microscopic Scales" (Grant No. GRAMS-815673) and the EU Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 101007855. Emanuele Berti is supported by NSF Grants No. AST-2006538, PHY-2207502, PHY-090003 and PHY-20043; by NASA Grants No. 20-LPS20-0011 and 21-ATP21-0010; by the John Templeton Foundation Grant 62840; and by the ITA-USA Science and Technology Cooperation program, supported by the Ministry of Foreign Affairs of Italy (MAECI). Richard Brito acknowledges financial support provided by FCT/Portugal under the Scientific Employment Stimulus - Individual Call - 2020.00470.CEECIND and under project No. 2022.01324.PTDC. Marta Colleoni, Sascha Husa, Anna Heffernan and Pierre Mourier are supported by the Spanish Agencia Estatal de Investigación grants PID2022-138626NB-I00, PID2019-106416GB-I00, IJC2019-041385, funded by MCIN/AEI/10.13039/501100011033; the MCIN with funding from the European Union NextGenerationEU/PRTR (PRTR-C17.I1); Comunitat Autonòma de les Illes Balears through the Direcció General de Recerca, Innovació I Transformació Digital with funds from the Tourist Stay Tax Law (PDR2020/11 - ITS2017-006), the Conselleria d'Economia, Hisenda i Innovació grant numbers SINCO2022/18146 and SINCO2022/6719, co-financed by the European Union and FEDER Operational Program 2021-2027 of the Balearic Islands; the "ERDF A way of making Europe"; Alvin J. K. Chua and Jonathan E. Thompson acknowledge support from the NASA LISA Preparatory Science grant 20-LPS20-0005. Katy Clough acknowledges funding from the UKRI Ernest Rutherford Fellowship (grant number ST/V003240/1). David A. Nichols acknowledges support from the NSF Grants No. PHY-2011784 and No. PHY-2309021. Vasileios Paschalidis is supported by NSF Grant No. PHY-2145421 and NASA Grant No. 80NSSC22K1605. Stuart Shapiro is supported by NSF Grants No. PHY-2006066 and PHY-2308242. Scott Field acknowledges support from US National Science Foundation Grants Nos. PHY-2110496, DMS-2309609, and by UMass Dartmouth's Marine and Undersea Technology (MUST) Research Program funded by the Office of Naval Research (ONR) under Grant No. N00014-23-1-2141. Davide Gerosa is supported by ERC Starting Grant No. 945155-GWmining, Cariplo Foundation Grant No. 2021-0555, MUR PRIN Grant No. 2022-Z9X4XS, Leverhulme Trust Grant No. RPG-2019-350, MSCA Fellowship No. 101064542-StochRewind, and the ICSC National Research Centre funded by NextGenerationEU. Eliu Huerta acknowledges support from the U.S. Department of Energy under Contract No. DE-AC02-06CH11357, and from the U.S. National Science Foundation (NSF) through award OAC-2209892. Scott A. Hughes has been supported by NASA ATP Grant 80NSSC18K1091, NSF Grants PHY-1707549 and PHY-2110384, by MIT's Margaret MacVicar Faculty Fellowship Program, and by the MIT Kavli Institute for Astrophysics and Space Research. Chris Kavanagh acknowledges support from Science Foundation Ireland under Grant number 21/PATH-S/9610. Gaurav Khanna acknowledges support from US National Science
Foundation Grants No. PHY-2307236 and DMS-2309609. Larry Kidder acknowledges support from NSF OAC-2209655, PHY-2308615 and Sherman Fairchild Foundation. Pablo Laguna acknowledges support from US National Science Foundation Grants No. PHY-2114582 and 2207780. Georgios Lukes-Gerakopoulos has been supported by the fellowship Lumina Quaeruntur No. LQ100032102 of the Czech Academy of Sciences. Hyun Lim is supported by the LANL Laboratory Directed Research and Development program under project number 20220087DR. LANL is operated by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE (Contract No. 89233218CNA000001). This work is authorized for unlimited release under LA-UR-23-31548. Tyson B. Littenberg is supported by the NASA LISA Study Office. Carlos O. Lousto gratefully acknowledge the National Science Foundation (NSF) for financial support from Grant No. PHY-1912632 and PHY-2207920. Elisa Maggio acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) - project number: 386119226. Richard O'Shaughnessy acknowledges support from NSF PHY-2012057, PHY-2309172, and AST-2206321. Naritaka Oshita is supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number JP23K13111. Rodrigo P. Macedo and Maarten van de Meent acknowledge the financial support by the VILLUM Foundation (grant No. VIL37766), the DNRF Chair program (grant No. DNRF162) by the Danish National Research Foundation, and the European Union's H2020 ERC Advanced Grant "Black holes: gravitational engines of discovery" grant agreement No. Gravitas-101052587. Adam Pound acknowledges the support of a Royal Society University Research Fellowship and a UKRI Frontier Research Grant under the Horizon Europe Guarantee scheme [grant number EP/Y008251/1]. Milton Ruiz acknowledges support from the Generalitat Valenciana Grant CIDEGENT/2021/046 and the Spanish Agencia Estatal de Investigación Grant PID2021-125485NB-C21. Carlos F. Sopuerta CFS is supported by contracts PID2019-106515GB-I00 and PID2022-137674NB-I00 (MCIN/AEI/10.13039/501100011033) and partially supported by the program *Unidad de Excelencia María de Maeztu* CEX2020-001058-M (MCIN/AEI/10.13039/501100011033). Stuart L. Shapiro acknowledges support from NSF Grants No. PHY-2006066 and No. PHY-2308242. Deirdre Shoemaker acknowledges support from NASA 22-LPS22-0023, 80NSSC21K0900 and NSF 2207780. Antonios Tsokaros is supported by NSF Grants No. PHY-2308242 and OAC-2310548. Niels Warburton acknowledges support from a Royal Society - Science Foundation Ireland University Research Fellowship. This publication has emanated from research conducted with the financial support of Science Foundation Ireland under Grant numbers 16/RS-URF/3428, 17/RS-URF-RG/3490 and 22/RS-URF-R/3825. Helvi Witek acknowledges support provided by the National Science Foundation under NSF Awards No. OAC-2004879 and No. PHY-2110416. Huan Yang is supported by the Natural Sciences and Engineering Research Council of Canada and in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of
Colleges and Universities. Miguel Zilhão acknowledges financial support by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e a Tecnologia) – references UIDB/04106/2020 and UIDP/04106/2020 – as well as FCT projects 2022.00721.CEECIND and 2022.04560.PTDC.

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