The gravitational-wave detectors LISA is one of the flagship missions of the European Space Agency planned to be launched in the 2030s. LISA will be sensitive mainly in the in the millihertz gravitational-wave band, and one of the most prominent and interesting sources in this band will be the so-called extreme mass ratio inspirals (EMRIs), where a comparatively light, stellar-mass compact object spirals into a super-massive black hole. The research goal of the PreciseEMRIs project was to contribute to the development of precise predictions of the signals emerging from these systems, and to prepare for the discovery of new fundamental science with LISA and other gravitational-wave detectors.

In particular, the overall objectives of the project were (1) to develop theoretical and mathematical tools to incorporate various new corrections to the evolution of EMRIs and gravitational-wave inspirals in general, (2) to synergize these existing frameworks with previous models used for gravitational-wave inspirals, (3) to describe and incorporate various astrophysical effects on the inspirals such as the effect of plasma swirling in the environment, or the gravity of the surrounding galaxy, and (4) to delve deep into the mathematical equations describing the problem and try to find various tricks to deal with them more efficiently and accurately. This project not only contributed a significant part of the work needed, but it also allowed the Researcher (Dr Vojtěch Witzany) to acquire the necessary skill and network to become an established scientist in the field of gravitational-wave theory.

The PreciseEMRIs project worked towards its Research objectives within 4 Work Packages (WPs). WP1 was concerned with devising and implementing a particularly elegant system of expressing the solutions of the EMRIs and various corrections, the so-called Action-angle formalism, the results of which were expressed in 2 code releases, 1 paper, and 1 monograph chapter, and several ongoing collaborations. The WP2 was then concerned with the implementation of the inspiral with various astrophysical effects, such as the swirling of plasma in the environment, the rotation of the object, or the gravity of objects outside of the system. The results of WP2 were expressed in 3 conference papers, 3 regular papers, and a code release. WP3 was then concerned with the formulation of new speculative theoretical ideas about treating the evolution of the gravitational field and its coupling to the inspiralling bodies, and it resulted in 1 regular paper.

The last WP4 was concerned with Management, Communication and Dissemination of the results, in the framework of which 10 conferences were attended, at which 6 talks were given, 3 plenary discussions led or co-led, and 1 poster presented by the Researcher. Additionally, the Researcher gave 7 research seminars at various institutions across the world, gave 1 Outreach talk, and wrote 2 Outreach articles. He also left a significant online footprint, with a number of posts on social media, Q&A websites, and developed or co-developed 2 websites related to the Action. Additionally, the researcher supervised or co-supervised 6 undergraduate research projects on topics related to the Action, thus disseminating the knowledge also in this way.

As detailed in Annex 1, the PreciseEMRIs project carried out in the framework of this Marie-Sklodowska Curie Action had the formal research objectives of (R1) developing a theoretical framework for incorporating gravitational self-force results, (R2) to synergize this framework with the existing effective one-body models, and (R3) to implement environmental and finite-size effects in the framework of (R1), (R4) to develop and discover new methods that could accelerate the current computations in gravitational self-force, and (R5) to analyse and develop an effective and efficient treatment of resonances in gravitational-wave inspirals. Additional objectives implied by Sections 1 and 2 of Annex 1 included the knowledge transfer between the host group and the research fellow, dissemination of the results, and the training and career broadening of the research fellow.   The research objectives have been addressed via four specific work packages: (WP1) was concerned with the development of an action-angle Hamiltonian for EMRIs, (WP2) with the modification of EMRIs due to various physical effects, (WP3) with the radiation of the Carter constant in EMRIs and possible simplifications. Additionally, (WP4) was concerned with the management, communication, and dissemination of these results. Significant strides towards the complete fulfilment of these objectives have been achieved during the action, and where possible, the work packages have been carried out to the full extent.

1.1  Explanation of the work carried per WP

Work carried out during the PreciseEMRIs fellowship fell within four specific work packages. This section summarizes the results and outputs of each work package (WP). The MSCA fellow worked in the Relativity group at the School of Mathematics and Statistics at University College Dublin (UCD) under the supervision of the PI Professor Adrian Ottewill and the other senior members of the group (Assoc. Prof. Barry Wardell, Assist. Prof. Niels Warburton), and in collegial contact with tenure-track members, postdocs, and PhD students in the group. Periodic meetings were set-up with the PI, while informal supervision was addressed during weekly meetings of the research group. During the course of the action, the MSCA fellow has also maintained collaborations and professional ties with his previous institutions (Astronomical Institute of the Czech Academy of Sciences, and the Institute of Theoretical Physics, Charles U. Prague). The achievements identified in this report reflect the excellent and welcoming environment of the host institution of the fellowship (UCD) but also the ongoing positive relations with the previous research environments in Prague.

1.2.1 Work Package 1

The purpose of the first work package was to build an action-angle formalism that would allow to incorporate existing results in the relativistic two-body problem. This was provided in the following manuscript:

·      Witzany, V. (2022). Action-angle coordinates for black-hole geodesics I: Spherically symmetric and Schwarzschild. ArXiv preprint submitted to Phys. Rev. D, arXiv:2203.11952.

The release of the manuscript was accompanied by a release of the corresponding formulas by using the platform GitHub:

·      Action-Angle-Schwarzschild on GitHub

Mathematica notebooks and .m files accompanying the paper on Action-angle coordinates for bound geodesics in spherically symmetric space-time. The code will be linked to a Zenodo repository once peer review of the paper is finished.

URL: https://github.com/VojtechW/Action-Angle-Schwarzschild

The above two items can be understood as a partial fulfilment of tasks (T1.2) and (T1.5). This is because the method constructs action-angle coordinates in generic spherically symmetric metrics, including the legacy Effective One-body model, which uses an effective spherically symmetric metric when both members of the inspiralling binary are non-rotating.

An important reference for the Researcher in task (T1.2) was the KerrGeodesics package developed as part of the BHPToolkit (bhptoolkit.org). In order to use it during the course of the action, he added a functionality that would become very useful in later tasks:

·      Initial conditions functionality for the KerrGeodesics package.

The KerrGeodesics package (part of the BHPToolkit initiative) provides functions to express analytical solutions of test particle motion near spinning black holes. This modification includes routines and analytical expressions that allow one to use this solution when one knows the initial position and velocity of the test particle. The code will be backed up to the Zenodo repository once the pull request into the master branch of KerrGeodesics is accepted.

Pull request into the main KerrGeodesics project: https://github.com/BlackHolePerturbationToolkit/KerrGeodesics/pull/38

Task (T1.4) was carried out in collaboration with Dr Gabriel Andres Piovano (currently postdoc at UCD) and is close to publication, task (T1.3) is currently underway with Dr Philip Lynch (AEI Potsdam-Golm), Dr Niels Warburton (UCD), and Dr Maarten van de Meent (Niels Bohr Inst. Copenhagen/AEI Potsdam-Golm). An additional part of task (T1.5) was to absorb information from numerical relativity, which is being investigated along with Dr. Aaron Zimmerman (U. Texas).

Task (T1.6) was concerned with the analytical treatment of resonances in EMRIs. This was successfully devised in the monograph chapter in collaboration with Dr Georgios Lukes-Gerakopoulos (Astronomical Inst., Czech Acad. Sci.):

·  Lukes-Gerakopoulos, G., Witzany, V. (2021). Nonlinear Effects in EMRI Dynamics and Their Imprints on Gravitational Waves. In: Bambi, C., Katsanevas, S., Kokkotas, K.D. (eds) Handbook of Gravitational Wave Astronomy. Springer, Singapore., arXiv:2103.06724.

A practical implementation of the treatment (T1.7) is underway in collaboration with Dr Philip Lynch (AEI Potsdam-Golm), Dr Niels Warburton (UCD), and Dr Maarten van de Meent (Niels Bohr Inst. Copenhagen/AEI Potsdam-Golm).

1.2.2 Work package 2

The aim of WP2 was to analyze and implement various modifications of the relativistic two-body problem either due to various astrophysical effects such as the rotation of the secondary or the interference of an accretion disk. A particularly strong line of research has been found in collaboration with a group of astronomers from institutions including the Massachusetts Institute of Technology, and the Astronomical Institute of the Czech Academy of Sciences, This resulted in the following publications and manuscripts.

·      Zajaček, M., Araudo, A., Karas, V., Czerny, B., Eckart, A., Suková, P., ... & Witzany, V. (2020). Missing bright red giants in the Galactic center: A fingerprint of its once active state?. In Stuchlík, Z., Törok, G. and Karas, V. (eds) Proceedings of RAGtime 22: Workshops on black holes and neutron stars. Silesian University in Opava, 2020, pp. 357–374. arXiv:2011.12868.

·      Suková, P., Zajaček, M., Witzany, V., & Karas, V. (2020). Perturbing the accretion flow onto a supermassive black hole by a passing star. In Stuchlík, Z., Törok, G. and Karas, V. (eds) Proceedings of RAGtime 22: Workshops on black holes and neutron stars. Silesian University in Opava, 2020, pp. 299–315. arXiv:2012.02608.

·      Suková, P., Zajaček, M., Witzany, V., & Karas, V. (2021). Stellar transits across a magnetized accretion torus as a mechanism for plasmoid ejection. The Astrophysical Journal, 917(1), 43. arXiv:2102.08135.

·      Pasham et al. (34 authors including Witzany, V.) (2022) A Case for a Binary Black Hole System Revealed via Quasi-Periodic Outflows, Research Square preprint submitted to Nature Astronomy, https://doi.org/10.21203/rs.3.rs-2230922/v1

In these works, we have examined various interactions of stellar-mass with accretion disks in the centres of galaxies and the observable effects this may have. In particular, the manuscript with Pasham et al. provides an example of an observed astronomical candidate for a system where such an object is truly interacting with the accretion disk. The work on these manuscripts can be seen as a fulfilment of tasks (T2.3) and (T2.5).

Task (2.4) was concerned with the effect external matter perturbations will have on EMRIs, and it was carried out in collaboration with Lukáš Polcar (currently PhD student at Charles U. Prague), and Georgios Lukes-Gerakopoulos (Astronomical Inst., Czech Acad. Sci.). This resulted in the following manuscript and code release:

·      Polcar, L., Lukes-Gerakopoulos, G., & Witzany, V. (2022). Extreme mass ratio inspirals into black holes surrounded by matter. Physical Review D, 106(4), 044069. ArXiv: 2205.08516.

·      Supplementary Maple notebooks to Polcar, L., Lukes-Gerakopoulos, G., & Witzany, V. (2022). Extreme mass ratio inspirals into black holes surrounded by matter. Physical Review D, 106(4), 044069.

Notebooks detailing the computations in the published paper, open access supplementary material on the website of the publisher of the paper. They also appear along with the open access version of the paper on arxiv.org.

URL1: https://journals.aps.org/prd/supplemental/10.1103/PhysRevD.106.044069/Canonical_perturbation_theory.mw

URL2: https://journals.aps.org/prd/supplemental/10.1103/PhysRevD.106.044069/Gravitational-wave_fluxes_.mw

The tasks (T2.2) and (T2.1) are currently underway in collaboration with Viktor Skoupý (currently PhD student at Charles U. Prague and Astronomical Institute, Czech Acad. Sci.). In the exploration of the topic and its various approaches, the following conference paper was written and published:

·      Witzany, V. (2023). Spinning particle: Is Newton-Wigner the only way?. In Proceedings of the MG16 Meeting on General Relativity Online; 5–10 July 2021 (pp. 4010-4018). https://doi.org/10.1142/9789811269776_0334

1.2.3 Work package 3

The proposal was submitted in September 2019. Coincidentally, the planned work in the work package was independently carried out by Grant & Flanagan in two papers published before the start of the action.[1] However, the study of the analogies between the electromagnetic and gravitational cases of the Carter constant and the Kerr space-time led the Researcher to some non-trivial conclusions about the relation between the two theories, which were summarized in the following manuscript:

·      Witzany, V. (2021). Einstein gravity as a theory with a SL (2, C) connection double copy. arXiv preprint submitted to Phys. Rev. D arXiv:2109.14607.

[1] Grant, A. M., & Flanagan, É. É. (2020). Conserved currents for electromagnetic fields in the Kerr spacetime. Classical and Quantum Gravity, 37(18), 185021.

Grant, A. M., & Flanagan, É. É. (2020). A class of conserved currents for linearized gravity in the Kerr spacetime. Classical and Quantum Gravity, 38(5), 055004.

1.2.4 Work package 4

This work package was concerned with management, communication, and dissemination, and it was planned in September 2019 while it was assumed that the fellowship would start in May 2020. Since the global Covid pandemic reached Europe in Spring 2020 and the fellowship started in September 2020, many of the Dissemination & Outreach activities were cancelled or moved online. Nevertheless, with these variations in mind, the broad formulation of WP4 was fulfilled. Specifically, 10 conferences were attended during the action, at which 6 talks were given, 3 plenary discussions led, and 1 poster presented by the Researcher. Additionally, the Researcher gave 7 research seminars at various institutions across the world, gave 1 Outreach talk, and wrote 3 Outreach articles. He also left a significant online footprint, with a number of posts on social media, Q&A websites, and developed or co-developed 2 websites related to the Action. A specific list of the activities is given below.

Talks given at conferences:

·      24th Capra Meeting on Radiation Reaction in General Relativity, 7-11. 6. 2021, Online/Perimeter Institute, Waterloo, Canada

Talk (11.6.): “Are we already observing inspirals into massive black holes?”

·      16th Marcel Grossmann meeting, 5-10.7. 2021, Online/Rome

Talk (5.7.): “Spinning particle: Is Newton-Wigner the only way?”

·      LISA Symposium XIV, 25-29. 6.2022, Glasgow/Online

Talk (pre-recorded): “Action-angle coordinates for black hole geodesics and their use in EMRIs”

·      23rd International Conference on General Relativity and Gravitation, 3-8. 7. 2022, Beijing

Talk (5.7.): “Action-angle coordinates for binary inspirals”

·  UK-V4 Frontiers of Science 10-11. 6. 2021 (invited), online

Talk (10.6.): “A small black hole falls into a big one: things get resonant”

·      High-Precision Gravitational Waves program (invited), 4.4.-10.6. 2022, Kavli Institute of Theoretical Physics, UC Santa Barbara, USA

Talk (2.6.): “Integrability in the relativistic two-body problem”

Leader/moderator of plenary discussions at conferences

·      24th Capra Meeting on Radiation Reaction in General Relativity, 7. – 11. 6. 2021, Online/Perimeter Institute, Waterloo, Canada

Discussion leader (11.6.): “Environmental effects”

·      25th Capra Meeting on Radiation Reaction in General Relativity, 20. – 24. 6. 2022, University College Dublin, local and scientific organizing committee

Discussion leader (21.6.): “Extended bodies”

Discussion leader (24.6.): “Resonances”

Posters at conferences:

·      WE-HERAEUS Seminar Gravitational Wave and Multimessenger Astronomy, 25-28. 4. 2022, Bad Honnef

Poster title: “Quasi-periodic oscillations in tidal disruption events as

markers of multimessenger sources?”

Organization of conferences:

·  21st BritGrav meeting, 12.-16. 4. 2021, University College Dublin/Online, local and scientific organizing committee, Judge for best student talk

·  25th Capra Meeting on Radiation Reaction in General Relativity, 20. – 24. 6. 2022, University College Dublin, local and scientific organizing committee

·  European Einstein Toolkit European meeting 2022, 29 August – 2 September, University College Dublin, local organizing committee

Seminars given:

·      Executive summary for LISA EMRI Work package telecon (invited), 22. 2. 2021 Online, shared talk with Georgios Lukes Gerakopoulos,

Title: “Nonlinear spin effects and prolonged resonances”

·      General Relativity and Astrophysics seminar 13. 4. 2021 (invited), Jagiellonian University Kraków

Title: “A small black hole falls into a big one: Resonances in extreme mass ratio inspirals”

·      Applied and Computational Mathematics seminar 11. 10. 2021, University College Dublin

Title: “Action-angle coordinates solve all your problems (with gravitational-wave inspirals)”

·      Relativistic seminar 21. 12. 2021, Institute of Theoretical Physics, Charles U. Prague

Title: “Action-angle coordinates for black-hole geodesics”

·      Relativity group seminar 17. 5. 2022 (invited), MIT Kavli Institute for astrophysics and space research, Cambridge, USA

Title: “Action-angle coordinates for binary inspirals”

·      Gravity seminar 14. 6. 2022 (invited), University Mississippi, Oxford, USA

Title: “Action-angle coordinates for black hole geodesics”

·      Relativistic seminar 25. 10. 2022, Institute of Theoretical Physics, Charles U. Prague

Title: “Resonances in Extreme mass ratio inspirals”

Outreach activities:

·      Outreach article: “UFO poblíž Chicaga” (“The UFO near Chicago” in Czech), 23.5. 2021 in Czech magazine Respekt (readership approximately 200 000). An article about the muon magnetic moment anomaly (g-2) announced by Fermilab and its implications.

·      Outreach article: “Nobelova cena za rok 2020: V centru naší galaxie je cosi temného a těžkého” (“Nobel Prize 2020: Something dark and heavy lurks in the centre of our galaxy” in Czech), Pokroky matematiky, fyziky a astronomie 66/4 (2021). Article about the half of the 2020 Nobel prize in Physics awarded to Reinhard Genzel and Andrea Ghez for the observations of the galactic centre black hole. Won 3rd prize for best article of 2021 in reader poll.

·      Outreach article:”Stín něžného obra” (“The shadow of the gentle giant” in Czech) 23.5. 2021 in Czech magazine Respekt (readership approximately 200 000). An article about the image of the black hole in the center of our Galaxy the Milky Way reconstructed by the Event Horizon Telescope collaboration.

·      Outreach talk: Science is Wonderful! 2021 (MSCA event), 21. 11. 2021, a virtual talk for a class of high-school students at Școala Excelsis, Chisinau, Moldova. Motivational talk about my work and life as a scientist with the title “Physics: from microwaves to black holes”

·      Online outreach: Sustained activity on the general-public Q&A website Physics Stackexchange (profile at https://physics.stackexchange.com/users/52394/void?tab=profile). 48 answers written during course of MSCA fellowship, and approximately 100 000 people reached during this period (according to website statistics).

·      Co-development of the long-term website of the Capra meeting, www.caprameeting.org, including, for example, its sections “For Students” (https://www.caprameeting.org/resources/for-students) which provides a list of resources for students looking to enter the sub-field

·      Founding accounts or maintaining an online presence on

o   GitHub (https://github.com/VojtechW/)

o   Google Scholar (https://scholar.google.com/citations?user=6ErvxkMAAAAJ)

o   InspireHEP (https://inspirehep.net/authors/1436457)

o   Publons/Web of Science (https://www.webofscience.com/wos/author/record/2144361)

o   ORCID (https://orcid.org/0000-0002-9209-5355)

o   Twitter (https://twitter.com/w_vojtech)

o   LinkedIn (https://twitter.com/w_vojtech)

o   personal website (www.witzany.science)

1.3 Impact

The PreciseEMRIs project had the expected impact both scientifically and career-wise for the Researcher. Following the project, starting January 2023, the Researcher was awarded the competitive Primus research fellowship from the Charles University in Prague. This 4-year fellowship is tied with financing for a small research team (one PhD student and two postdocs), thus moving the Researcher from the Euraxess class of Recognized Researcher (R2) to an early Established Researcher (R3). This was made possible also thanks to the wide array of networking and training opportunities that the Researcher had access to during the PreciseEMRIs project.

Apart from the significant network boost caused simply by the continuous contact with the Relativity group in Dublin and its guests, the Researcher also conducted the following stays (for the attendance of conferences see Section 1.2.4 of this document). These visits all had financial contributions from the host institutions as well as from the funds from the project:

·      15. 5. – 22.5. 2022, MIT Kavli Institute for Astrophysics and Space Research, Cambridge, Massachusetts, Visit to the relativity group of Scott Hughes and informal visit to the nearby Harvard Center for Astrophysics.

·      23.5. – 10. 6. 2022, Kavli Institute of Theoretical Physics, UC Santa Barbara, USA.  Resident for the Kavli research program „High-Precision Gravitational Waves“.

·      13.6. – 17. 6. 2022, University of Mississippi, Oxford, Mississippi, Collaborative visit to the group of Leo Stein.

Other training and networking opportunities the Researcher attended (while not presenting a talk or seminar to be listed in Section 1.1.4) included:

·      The Lorentz Centre Workshop on Gravitational Wave Astrophysics for Early Career Scientists, 3.-7. 5. 2021, Online.

·      Advances in Computational Relativity semester program 9. 9. – 11. 12. 2021 (realized mainly through a series of week-long online workshop throughout the semester), Online/Institute for Computational and Experimental Research in Mathematics, Brown University, Rhode Island, USA.

To gain mentoring experience, the Researcher has supervised the following undergraduate students at UCD:

·  David Dwyer (Autumn 2020 – Spring 2021), MA Thesis “Dynamics of Binary Black Hole systems”.

·      Maxime Gaudioux (Summer 2021, co-supervision with Niels Warburton) Undergraduate Summer Research project “Relativistic model for tidal disruptions” rewarded with 1600 EUR stipend.

·      Brian Sheridan (Autumn 2021 – Spring 2022, co-supervision with Sarp Akcay), MA Thesis “Parameter Estimation for the OJ287 Binary Black Hole System”.

·      Jonathan Broome (Autumn 2021 – Spring 2022), MSc. Thesis “Equations of motion of a point particle in curved space-time: To second order in particle mass”.

·      Adam Keyes & Brian Sheridan (Summer 2022, co-supervision with Sarp Akcay), Undergraduate Summer Research project “Parameter Estimation for OJ 287” rewarded with 1600 EUR stipend for each of the two students.

Another key aspect of the training of the Researcher was the journal club of the Relativity group. He founded and led the weekly journal club in collaboration with the Relativity group (managed through the Benty fields website, see https://www.benty-fields.com/manage_jc?groupid=525). By both reviewing the current literature himself and by coaching the junior members of the group, the Researcher deepened and broadened his knowledge of the state of the art within the field, while also strengthening his skills in mentoring and leadership.

Additionally, to broaden his career, the Researcher attended the “Teaching & Learning Seminar Series for Postdocs” (5 2-hour interactive sessions) provided by UCD in December 2020. As a result, he decided to deepen his teaching experience by teaching the course ACM 40750, General Relativity & Black Holes in the Spring Trimester of 2021. The teaching was accompanied by meetings with the module coordinator Dr Wardell and Prof. Ottewill (PI) where the teaching experience and process was discussed, so that the activity would have a strong training aspect for the Researcher. These meetings included the discussion of the curriculum, various forms of continuous assessment, load on students, and how to treat student feedback. This qualification was one of the key aspects for the Researcher to get his current tenure-track position at Charles U. Prague.

Dissemination and Outreach were a part of WP4 (see Section 1.1.4 of this document). The general goals of this Work Package were fulfilled despite the challenges imposed by the fact that half of the action was carried out during Covid 19 lockdowns and many of the activities had to be replaced by virtual alternatives.

3. Update of the data management plan (if applicable)

As described in the Data Management Plan (submitted as a Deliverable during the course of the Action) the main output of the PreciseEMRIs project were mathematical theory and predictions. These were documented in the published peer-reviewed papers and preprints on arXiv.org (see Section 2 of this document). Additionally, where possible the codes detailing the methods and the computations were published using either GitHub or tools provided by the publishers of the journals. The codes on GitHub will be backed up by the automatic GitHub linking tools to the OpenAIRE infrastructure Zenodo once the various forms of peer review detailed in Section 2 are concluded.

4. Follow-up of recommendations and comments from previous review(s) (if applicable)

Not applicable as this is the first and concluding report for the MSCA IF.

5. Deviations from Annex 1 and Annex 2 (if applicable)

The proposal of the PreciseEMRIs project was planned out and written before the submission in September 2019, while the action itself started in September 2020, after the world was unexpectedly hit by the global Covid-19 pandemic in Spring 2020. The general approach of the Irish government to the pandemic was conservative – to impose strict physical distancing and other non-pharmaceutical measures, and to limit unnecessary in-person contact during most of 2020-2021. The first partial loosening of measures started in the second half of 2021 when most of the population reached full vaccination against Covid 19, and it can be estimated that the possibilities of networking and in-person contact for the Researcher that were assumed in Annex 1 and 2 were only recovered in Spring 2022 after the roll-out of Covid vaccine booster doses (roughly 18 months after the start of the action).

Naturally, this led to a modification of several details of the PreciseEMRIs project, while keeping and fulfilling the broad ideas and goals. For example, most of the meetings of 2020 to early 2021 had to be carried out remotely via videocalls or similar, with less space for informal networking and informal knowledge transfer. Relocating to the Dublin location and various administrative tasks connected with the mobility were often more difficult and time demanding during the pandemic (for example, obtaining a Personal Public Services number or the European Health Insurance Card from the Irish government was accompanied with significant delays due to the situation).

The Researcher and the Relativity group mitigated the situation by setting up a weekly virtual group meetings and the Journal club, even setting up virtual social events or occasional outdoor meetings (in line with the government regulations at the time). The Researcher also prioritized tasks that could be worked on in collaboration with his previous scientific network while slowly establishing ties at UCD. Additionally, the Irish Higher Education Authority provided the Researcher with funding to extend his stay at UCD by 4 months beyond the original duration of the action until December 2022 in order to compensate the impacts of the lockdowns in the first half of the fellowship. 

5.1 Tasks

The Tasks planned and proposed in WP1-WP3 within the PreciseEMRIs project were a series of high-risk/high-potential ideas for theoretical research. As such, it was inherently difficult to plan their time-commitment or viability. Even though extensive care had been given by the Researcher to only propose ideas that were viable, the nature of the research inevitably led to some isolated cases where further exploration showed that the research idea was not viable enough to give results of adequate scientific value or too time intensive to be worked out fully during the 24-month project. Other issues arose from the fact that the viable, relevant, and timely ideas presented in the plan of the PreciseEMRIs project (submitted a year before the start of the action) were also identified as such, and worked on in parallel, by competing scientists in the field. In some cases, the competing scientists were able to exhaust the potential of the ideas before the Researcher. Furthermore, the viability of the plan of the PreciseEMRIs project relied on collaboration with other researchers, which was sometimes slower to establish due to the Covid-19 situation described in the previous Section.

On the other hand, other unexpected excellent opportunities arose due to new scientific discoveries and unexpected collaboration opportunities. An example of this was the first detections of the novel astronomical phenomena of quasi-periodic eruptions and quasi-periodic outflows in active galactic nuclei in 2019 and 2022, and the collaboration with the astronomy teams detailed in Section 1.1.2.