## Final Report Summary - EGO (Exploiting Gravitational-Wave Observations: Modeling Coalescing Black Hole Binaries and Extreme Mass Ratio Inspirals)

The existence of gravitational radiation is one of the most important predictions of Einstein's general theory of relativity. Since 2015, the first direct detections of gravitational waves from coalescing black hole and neutron star binaries has herald a new era in astronomy. By the end of this decade, an increasingly sensitive network of kilometer-scale, ground-based laser interferometers such as Advanced Virgo and GEO-HF in Europe, Advanced LIGO in the USA and KAGRA in Japan will detect up to several hundreds of such events per year.

Moreover, the spectacular success of LISA Pathfinder in 2016 has paved the way for ESA’s Laser Interferometer Space Antenna (LISA), which will target mHz frequencies, and thus the coalescence of supermassive black holes, and the inspiral of stellar mass compact objects into massive black holes, dubbed extreme mass-ratio inspirals.

Over the coming decades, the emerging field of gravitational-wave astronomy is bound to have a tremendous impact on astrophysics, cosmology and fundamental physics. In particular, future gravitational-wave observations will not only tell us about the underlying population of binary black holes, but also allow testing the general theory of relativity, and improve our understanding of the dynamics of compact binary systems in a highly dynamical, strong-field regime.

However, upon arrival on Earth, the typical amplitude of the gravitational waves generated by such astrophysical sources is exceedingly small. Hence the detection and analysis of these signals require very accurate theoretical predictions, for use as “template waveforms” to be cross-correlated against the output of the detectors. These gravitational waveforms can be modelled by means of various approximation methods in general relativity, such as the post-Newtonian formalism, black hole perturbation theory and the gravitational self-force framework, the effective one-body model, and numerical relativity simulations.

The primary objective of this research project was to develop highly-accurate and physically-motivated "gravitational waveforms" that would model the gravitational-wave emission from all binary systems of compact objects. More precisely, these waveforms would be used for data analysis purposes, in both ground-based and space-based observatories, to detect and analyze gravitational-wave signals from stellar-mass compact binaries, intermediate mass-ratio inspirals, supermassive black hole binaries, and extreme mass-ratio inspirals. To achieve this goal, three lines of research were pursued:

(i) Comparing the predictions from a variety of analytical approximations schemes (post-Newtonian theory, black hole perturbation theory, gravitational self-force, effective one-body model) and numerical relativity simulations in general relativity;

(ii) Extending the so-called first law of compact binary mechanics beyond the simplest case of non-spinning compact bodies moving along circular orbits; and

(iii) Developing a new class of hybrid waveforms relying on the predictions of black hole perturbation theory for the inspiral part of the motion and on numerical relativity waveforms for the last orbits, merger and final ringdown.

During the course of this project, significant progress has been made towards achieving the objectives (i) and (ii). In particular, the main results obtained include:

(1) The first comparison of the predictions of the post-Newtonian approximation and black hole perturbation theory for the dynamics of binary systems of compact objects for non-circular orbits;

(2) A comparison of the predictions from numerical relativity simulations, the post-Newtonian approximation and black hole perturbation theory, based on the computation of the horizon surface gravity in co-rotating black hole binaries;

(3) The calculation of the shift in the frequency of the Kerr innermost stable circular equatorial orbit induced by the conservative piece of the gravitational self-force acting on the particle;

(4) The development of a Hamiltonian formulation of the dynamics of a massive point particle in the Kerr geometry that accounts for all of the effects of the conservative gravitational self-force.

(5) An extension of the first law of binary mechanics to generic bound (eccentric) orbits for non-spinning compact objects, including the leading effects of gravitational-wave tails;

(6) Partial results have also been obtained for generic, precessing spinning binaries, and for the inclusion of quadrupolar deformations in the particular case of circular orbits.

Moreover, the spectacular success of LISA Pathfinder in 2016 has paved the way for ESA’s Laser Interferometer Space Antenna (LISA), which will target mHz frequencies, and thus the coalescence of supermassive black holes, and the inspiral of stellar mass compact objects into massive black holes, dubbed extreme mass-ratio inspirals.

Over the coming decades, the emerging field of gravitational-wave astronomy is bound to have a tremendous impact on astrophysics, cosmology and fundamental physics. In particular, future gravitational-wave observations will not only tell us about the underlying population of binary black holes, but also allow testing the general theory of relativity, and improve our understanding of the dynamics of compact binary systems in a highly dynamical, strong-field regime.

However, upon arrival on Earth, the typical amplitude of the gravitational waves generated by such astrophysical sources is exceedingly small. Hence the detection and analysis of these signals require very accurate theoretical predictions, for use as “template waveforms” to be cross-correlated against the output of the detectors. These gravitational waveforms can be modelled by means of various approximation methods in general relativity, such as the post-Newtonian formalism, black hole perturbation theory and the gravitational self-force framework, the effective one-body model, and numerical relativity simulations.

The primary objective of this research project was to develop highly-accurate and physically-motivated "gravitational waveforms" that would model the gravitational-wave emission from all binary systems of compact objects. More precisely, these waveforms would be used for data analysis purposes, in both ground-based and space-based observatories, to detect and analyze gravitational-wave signals from stellar-mass compact binaries, intermediate mass-ratio inspirals, supermassive black hole binaries, and extreme mass-ratio inspirals. To achieve this goal, three lines of research were pursued:

(i) Comparing the predictions from a variety of analytical approximations schemes (post-Newtonian theory, black hole perturbation theory, gravitational self-force, effective one-body model) and numerical relativity simulations in general relativity;

(ii) Extending the so-called first law of compact binary mechanics beyond the simplest case of non-spinning compact bodies moving along circular orbits; and

(iii) Developing a new class of hybrid waveforms relying on the predictions of black hole perturbation theory for the inspiral part of the motion and on numerical relativity waveforms for the last orbits, merger and final ringdown.

During the course of this project, significant progress has been made towards achieving the objectives (i) and (ii). In particular, the main results obtained include:

(1) The first comparison of the predictions of the post-Newtonian approximation and black hole perturbation theory for the dynamics of binary systems of compact objects for non-circular orbits;

(2) A comparison of the predictions from numerical relativity simulations, the post-Newtonian approximation and black hole perturbation theory, based on the computation of the horizon surface gravity in co-rotating black hole binaries;

(3) The calculation of the shift in the frequency of the Kerr innermost stable circular equatorial orbit induced by the conservative piece of the gravitational self-force acting on the particle;

(4) The development of a Hamiltonian formulation of the dynamics of a massive point particle in the Kerr geometry that accounts for all of the effects of the conservative gravitational self-force.

(5) An extension of the first law of binary mechanics to generic bound (eccentric) orbits for non-spinning compact objects, including the leading effects of gravitational-wave tails;

(6) Partial results have also been obtained for generic, precessing spinning binaries, and for the inclusion of quadrupolar deformations in the particular case of circular orbits.