## Periodic Report Summary 1 - EGO (Exploiting Gravitational-Wave Observations: Modeling Coalescing Black Hole Binaries and Extreme Mass Ratio Inspirals)

The primary objective of this research project is to develop highly-accurate and physically-motivated "gravitational waveforms" that will model the gravitational-wave emission from all binary systems of compact objects. The development of such waveforms is a prerequisite for the full scientific exploitation of current and future ground-based and space-based gravitational-wave observatories.

More precisely, these waveforms will 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, super-massive black hole binaries, and extreme mass-ratio inspirals. This goal will be reached by:

(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;

(ii) Extending the so-called first law of binary black hole 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.

So far, significant progress has been made towards achieving the objectives (i) and (ii). In particular, the main results obtained so far 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) 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;

(3) An extension of the first law of binary mechanics to generic bound (eccentric) orbits for non-spinning compact objects, as well as partial results in the case of fully generic, precessing spinning binaries; and

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

More precisely, these waveforms will 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, super-massive black hole binaries, and extreme mass-ratio inspirals. This goal will be reached by:

(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;

(ii) Extending the so-called first law of binary black hole 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.

So far, significant progress has been made towards achieving the objectives (i) and (ii). In particular, the main results obtained so far 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) 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;

(3) An extension of the first law of binary mechanics to generic bound (eccentric) orbits for non-spinning compact objects, as well as partial results in the case of fully generic, precessing spinning binaries; and

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

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Life Sciences**Record Number**: 187618 /

**Last updated on**: 2016-08-22