On the equations of motion of point-particle binaries at the third post-Newtonian order

Abstract

We investigate the dynamics of two point-like particles through the third post-Newtonian (3PN) approximation of general relativity. The infinite self-field of each point-mass is regularized by means of Hadamard's concept of ``partie finie''. Distributional forms associated with the regularization are used systematically in the computation. We determine the stress-energy tensor of point-like particles compatible with the previous regularization. The Einstein field equations in harmonic coordinates are iterated to the 3PN order. The 3PN equations of motion are Lorentz-invariant and admit a conserved energy (neglecting the 2.5PN radiation reaction). They depend on an undetermined coefficient, in agreement with an earlier result of Jaranowski and Schaefer. This suggests an incompleteness of the formalism (in this stage of development) at the 3PN order. In this paper we present the equations of motion in the center-of-mass frame and in the case of circular orbits.

12 pages, to appear in Physics Letters A, minor changes included

References in corpus (1)

• Hadamard Regularization

Cited by in corpus (104)

• The Confrontation between General Relativity and Experiment
• An Effective Field Theory of Gravity for Extended Objects
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• The Confrontation between General Relativity and Experiment
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
• High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Dimensional regularization of the gravitational interaction of point masses
• A Comparison of search templates for gravitational waves from binary inspiral
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
• The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. II. Two-body equations of motion to second post-Newtonian order, and radiation-reaction to 3.5 post-Newtonian order
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Phasing of gravitational waves from inspiralling eccentric binaries
• Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order
• A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects
• Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description
• Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• Remnant Masses, Spins and Recoils from the Merger of Generic Black-Hole Binaries
• Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Hadamard Regularization
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Effective field theory methods to model compact binaries
• Effective field theory calculation of second post-Newtonian binary dynamics
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Tidal Effects in the Post-Minkowskian Expansion
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems
• Innermost circular orbit of binary black holes at the third post-Newtonian approximation
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
• Circular orbits of corotating binary black holes: comparison between analytical and numerical results
• Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. III. Identical and different mass stars with gamma=2
• Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates
• Equation of motion for relativistic compact binaries with the strong field point particle limit : the second and half post-Newtonian order
• A comparison of search templates for gravitational waves from binary inspiral - 3.5PN update
• Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits
• Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations
• Mining the Geodesic Equation for Scattering Data
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Statistical studies of Spinning Black-Hole Binaries
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• First Law of Mechanics for Black Hole Binaries with Spins
• Lorentzian regularization and the problem of point-like particles in general relativity
• Accuracy of gravitational waveform models for observing neutron-star--black-hole binaries in Advanced LIGO
• Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?
• Gravitational Faraday effect from on-shell amplitudes
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
• Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
• Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion
• Ineffectiveness of Padé resummation techniques in post-Newtonian approximations
• Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
• A skeleton approximate solution of the Einstein field equations for multiple black-hole systems
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Surface-integral expressions for the multipole moments of post-Newtonian sources and the boosted Schwarzschild solution
• New class of post-Newtonian approximants to the waveform templates of inspiralling compact binaries: Test-mass in the Schwarzschild spacetime
• Testing pseudo-complex general relativity with gravitational waves
• On the equation of motion of compact binaries in Post-Newtonian approximation
• Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates
• A New Template Family For The Detection Of Gravitational Waves From Comparable Mass Black Hole Binaries
• Gravitational waves from inspiraling binary black holes
• Probing Particle Physics with Gravitational Waves
• General Relativistic Dynamics of Compact Binary Systems
• Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation
• Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order
• Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies
• Equations of motion of compact binaries at the third post-Newtonian order
• On the two-body problem in general relativity