Compact binary coalescence (CBC)

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Table of contents

Acknowledgements
Introduction
1 Introduction to gravitational waves and to the linearized theory of general relativity
1.1 Short history of the theory of gravitational waves
1.2 The linearized theory of general relativity and gravitational waves
1.2.1 The linearized Einstein equations
1.2.2 Gravitational wave solution to the vacuum linearized Einstein equations
1.2.3 Effect of gravitational waves on matter
1.3 The Einstein quadrupole formulae
1.3.1 Einstein quadrupole formulae for the energy and angular momentum fluxes
1.3.2 Some applications of the Einstein quadrupole formulae and orders of magnitude
1.4 The confirmation with radio-astronomy of the Einstein quadrupole formulae .
1.4.1 Neutron stars, pulsars, and pulsar binary systems
1.4.2 Evolution of the orbits
2 Detection of gravitational waves
2.1 Detection of GW with laser interferometry
2.1.1 History: from the Weber bars to the interferometer detectors.
2.1.2 Ground-based interferometry
2.1.3 LISA and space-based interferometry
2.1.4 Summary of the current and future network of GW observatories .
2.2 Possible sources
2.2.1 Continuous compact binary systems
2.2.2 Compact binary coalescence (CBC)
2.2.3 Super Massive Black Hole Binary
2.2.4 Extreme mass ratio inspiral (EMRI)
2.2.5 Supernovae
2.2.6 Continuous wave
2.2.7 Stochastic background
2.3 Template building and match filtering
2.3.1 Matched filtering
2.3.2 Post-Newtonian theory
2.3.3 Numerical relativity
2.3.4 Studying the ringdown with black hole perturbation
2.3.5 The self-force framework
2.3.6 Building the template with Effective-One-Body and IMRPhenomD .
2.4 First detections
2.4.1 Runs O1 and O2
2.4.2 The first direct detection of gravitational waves: GW150914
2.4.3 The first detection of NS-NS coalescence: GW170817
2.4.4 Summary
3 Introduction to post-Newtonian theory
3.1 Introduction to post-Newtonian theory
3.2 The equations of motion: a historical review
3.2.1 1PN, 2PN and 2.5PN
3.2.2 3PN and 3.5PN
3.2.3 4PN and 4.5PN
3.3 Spins
3.3.1 Formalism
3.3.2 State-of-the-art
3.4 The 4.5PN Project
4 The far-zone radiative field and the gravitational wave flux
4.1 The multipolar post-Minkowskian algorithm
4.1.1 The Einstein multipolar post-Minkowskian equations
4.1.2 Solving the MPM Einstein equations in the linear case
4.1.3 The MPM algorithm at any order n
4.1.4 A useful notation
4.2 An explicit computation of the tails
4.2.1 A computation step by step of hμ (2)M×Mij .
4.2.2 Non-locality: the appearance of the tails
4.2.3 Computation of the tails-of-tails and the tails-of-tails-of-tails
4.2.4 Explicit closed-form representations of the solution
4.2.5 Formulae to integrate the tails-of-tails-of-tails
4.2.6 Result
4.3 Going to radiative coordinates and flux derivation
4.3.1 Going to radiative coordinates
4.3.2 The radiative multipole moments
4.3.3 Deriving the equation for the flux
4.3.4 The flux at 4.5PN for circular orbits
5 The matching equation and its consequences
5.1 Near zone, far zone, buffer zone and notations
5.2 The Finite Part regularization and propagators
5.2.1 Finite Part
5.2.2 g−1 ret , g−k and gI−1
5.3 The matching equation
5.3.1 Two useful lemmas
5.3.2 The matching equation and its consequences
5.4 Explicit expressions of the source moment multipoles
6 Ambiguity-free equations of motion at the 4PN order
6.1 Presentation of the Fokker Lagrangian method
6.1.1 The method
6.1.2 UV regularization using Hadamard partie finie regularization
6.1.3 UV regularization using dimensional regularization
6.1.4 Infra-red regularization
6.1.5 Adding the tail effects in 3 dimensions
6.1.6 A first result in disagreement with self-force computation
6.2 The systematic use of dimensional regularization
6.2.1 Infra-red dimensional regularization
6.2.2 The tails in d dimensions
6.2.3 Conclusion
7 Conserved quantities and equations of motion in the center of mass
7.1 Conserved integrals of the motion
7.1.1 The center of mass
7.1.2 Equations of motion in the center of mass frame
7.1.3 Lagrangian in the center of mass frame
7.1.4 Energy and angular momentum in the center of mass frame
7.2 Circular orbit and dissipative effects
7.2.1 Effects of the tails
7.2.2 Circular orbit
7.2.3 Dissipative effects
8 Computing the source mass quadrupole moment at 4PN
8.1 Expression of the mass quadrupole as a function of the potentials
8.1.1 General introduction
8.1.2 Generalization in d dimensions
8.1.3 Metric in d dimensions
8.1.4 Simplification of the result
8.2 Integrating the different terms
8.2.1 Integrating the compact support terms
8.2.2 μ1 and ˜μ1
8.2.3 Integrating the surface terms
8.2.4 Integrating the non-compact terms
8.3 Computing the potentials
8.3.1 Summary of the potentials required
8.3.2 Computing the potentials in 3 dimensions
8.3.3 Performing correctly the matching
8.3.4 Known formulae in d dimensions
8.3.5 Superpotentials
8.3.6 Potentials at the locations of the point particles
8.3.7 Potentials at infinity
8.4 Results
8.4.1 A preliminary result
8.4.2 Checks and perspectives
Conclusion
A Conventions and notations
A.1 Indices and summation convention
A.2 The Einstein equations
A.3 Multiple indices
A.4 Geometrical variables
B 4PN Fokker Lagrangian
B.1 The Fokker Lagrangian
B.2 Shifts applied
B.2.1 Shift
B.2.2 Shift
B.2.3 Shift
C The mass quadrupole as a function of the potentials
Bibliography