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Note: Intro -- Contents -- List of figures -- Preface -- The general relativistic two-body problem -- 1 Introduction -- 2 Multichart approach to the N-body problem -- 3 EOB description of the conservative dynamics of two-body systems -- 4 EOB description of radiation reaction and of the emitted waveform during inspiral -- 5 EOB description of the merger of binary black holes and of the ringdown of the final black hole -- 6 EOB vs NR -- 6.1 EOB[NR] waveforms vs NR ones -- 6.2 EOB[3PN] dynamics vs NR one -- 7 Other developments -- 7.1 EOB with spinning bodies -- 7.2 EOB with tidally deformed bodies -- 7.3 EOB and GSF -- 8 Conclusions -- References -- Hamiltonian dynamics of spinning compact binaries through high post-Newtonian approximations -- 1 Introduction -- 2 Hamiltonian formulation of general relativity -- 2.1 Point particles -- 2.2 Spinning particles -- 2.3 Introducing the Routhian -- 3 The Poincaré algebra -- 4 Post-Newtonian binary Hamiltonians -- 4.1 Spinless binaries -- 4.2 Spinning binaries -- 5 Binary motion -- 5.1 Spinless two-body systems -- 5.2 Particle motion in Kerr geometry -- 5.3 Two-body systems with spinning components -- References -- Covariant theory of the post-Newtonian equations of motion of extended bodies -- 1 Introduction -- 2 A theory of gravity for post-Newtonian celestial mechanics -- 2.1 The field equations -- 2.2 The energy-momentum tensor -- 3 Parameterized post-Newtonian celestial mechanics -- 3.1 External and internal problems of motion -- 3.2 Solving the field equations by post-Newtonian approximations -- 3.3 The post-Newtonian field equations -- 3.4 Conformal harmonic gauge -- 4 Parameterized post-Newtonian coordinates -- 4.1 The global post-Newtonian coordinates -- 4.2 The local post-Newtonian coordinates -- 5 Post-Newtonian coordinate transformations by asymptotic matching. , 5.1 General structure of the transformation -- 5.2 Matching solution -- 6 Post-Newtonian equations of motion of extended bodies in local coordinates -- 6.1 Microscopic post-Newtonian equations of motion -- 6.2 Post-Newtonian mass of an extended body -- 6.3 Post-Newtonian center of mass and linear momentum of an extended body -- 6.4 Translational equation of motion in the local coordinates -- 7 Post-Newtonian equations of motion of extended bodies in global coordinates -- 7.1 STF expansions of the external gravitational potentials in terms of the internal multipoles -- 7.2 Translational equations of motion -- 8 Covariant equations of translational motion of extended bodies -- 8.1 Effective background manifold -- 8.2 Geodesic motion and 4-force -- 8.3 Four-dimensional form of multipole moments -- 8.4 Covariant translational equations of motion -- 8.5 Comparison with Dixon's translational equations of motion -- References -- On the DSX-framework -- 1 Introduction -- 2 The post-Newtonian formalism -- 2.1 The general form of the metric -- 3 Field equations and the gauge problem -- 4 The gravitational field of a body -- 4.1 Post-Newtonian multipole moments -- 5 Geodesic motion in the PN-Schwarzschild field -- 6 Astronomical reference frames -- 6.1 Transformation between global and local systems: first results -- 6.2 Split of local potentials, multipole moments -- 6.3 Tetrad induced local coordinates -- 6.4 The standard transformation between global and local coordinates -- 6.5 The description of tidal forces -- 7 The gravitational N-body problem -- 7.1 Local evolution equations -- 7.2 The translational motion -- 8 Further developments -- References -- General relativistic theory of light propagation in multipolar gravitational fields -- 1 Introduction -- 1.1 Statement of the problem -- 1.2 Historical background -- 1.3 Notations and conventions. , 2 The metric tensor, gauges and coordinates -- 2.1 The canonical form of the metric tensor perturbation -- 2.2 The harmonic coordinates -- 2.3 The ADM coordinates -- 3 Equations of propagation of electromagnetic signals -- 3.1 Maxwell equations in curved spacetime -- 3.2 Maxwell equations in the geometric optics approximation -- 3.3 Electromagnetic eikonal and light-ray geodesics -- 3.4 Polarization of light and the Stokes parameters -- 4 Mathematical technique for analytic integration of light-ray equations -- 4.1 Monopole and dipole light-ray integrals -- 4.2 Light-ray integrals from quadrupole and higher order multipoles -- 5 Gravitational perturbations of the light ray -- 5.1 Relativistic perturbation of the electromagnetic eikonal -- 5.2 Relativistic perturbation of the coordinate velocity of light -- 5.3 Perturbation of the light-ray trajectory -- 6 Observable relativistic effects -- 6.1 Gravitational time delay of light -- 6.2 Gravitational deflection of light -- 6.3 Gravitational shift of frequency -- 6.4 Gravity-induced rotation of the plane of polarization of light -- 7 Light propagation through the field of gravitational lens -- 7.1 Small parameters and asymptotic expansions -- 7.2 Asymptotic expressions for observable effects -- 8 Light propagation through the field of plane gravitational waves -- 8.1 Plane-wave asymptotic expansions -- 8.2 Asymptotic expressions for observable effects -- References -- On the backreaction problem in cosmology -- 1 Introduction -- 2 Formulation and averaging -- 3 Calculation in the Newtonian gauge -- 4 Definition of the background -- 5 Conclusions -- References -- Post-Newtonian approximations in cosmology -- 1 Introduction -- 2 Derivatives on the geometric manifold -- 2.1 Variational derivative -- 2.2 Lie derivative -- 3 Lagrangian and field variables -- 3.1 Action functional. , 3.2 Lagrangian of the ideal fluid -- 3.3 Lagrangian of scalar field -- 3.4 Lagrangian of a localized astronomical system -- 4 Background manifold -- 4.1 Hubble flow -- 4.2 Friedmann-Lemître-Robertson-Walker metric -- 4.3 Christoffel symbols and covariant derivatives -- 4.4 Riemann tensor -- 4.5 The Friedmann equations -- 4.6 Hydrodynamic equations of the ideal fluid -- 4.7 Scalar field equations -- 4.8 Equations of motion of matter of the localized astronomical system -- 5 Lagrangian perturbations of FLRW manifold -- 5.1 The concept of perturbations -- 5.2 The perturbative expansion of the Lagrangian -- 5.3 The background field equations -- 5.4 The Lagrangian equations for gravitational field perturbations -- 5.5 The Lagrangian equations for dark matter perturbations -- 5.6 The Lagrangian equations for dark energy perturbations -- 5.7 Linearized post-Newtonian equations for field variables -- 6 Gauge-invariant scalars and field equations in 1+3 threading formalism -- 6.1 Threading decomposition of the metric perturbations -- 6.2 Gauge transformation of the field variables -- 6.3 Gauge-invariant scalars -- 6.4 Field equations for the scalar perturbations -- 6.5 Field equations for vector perturbations -- 6.6 Field equations for tensor perturbations -- 6.7 Residual gauge freedom -- 7 Post-Newtonian field equations in a spatially flat universe -- 7.1 Cosmological parameters and scalar field potential -- 7.2 Conformal cosmological perturbations -- 7.3 Post-Newtonian field equations in conformal spacetime -- 7.4 Residual gauge freedom in the conformal spacetime -- 8 Decoupled system of the post-Newtonian field equations -- 8.1 The universe governed by dark matter and cosmological constant -- 8.2 The universe governed by dark energy -- 8.3 Post-Newtonian potentials in the linearized Hubble approximation -- 8.4 Lorentz invariance of retarded potentials. , 8.5 Retarded solution of the sound-wave equation -- References -- Index.