Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order

Abstract

An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3 PN acceleration of the binary orbital motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting equation of motion admits a conserved energy (neglecting the 2.5 PN radiation reaction effect), is Lorentz invariant and is unambiguous: there exist no undetermined parameter reported in the previous works. We shall show that our 3 PN equation of motion agrees physically with the Blanchet and Faye 3 PN equation of motion if $\lambda =-1987/3080$, where $\lambda$ is the parameter which is undetermined within their framework. This value of $\lambda$ is consistent with the result of Damour, Jaranowski, and Schäfer who first completed a 3 PN iteration of the ADM Hamiltonian in the ADMTT gauge using the dimensional regularization.

arXiv comment52 pages, no figure, Appendices B and D added. Phys. Rev. D in press

References in corpus (34)

• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
• Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
• Dimensional regularization of the gravitational interaction of point masses
• Detector Description and Performance for the First Coincidence Observations between LIGO and GEO
• Stable Operation of a 300-m Laser Interferometer with Sufficient Sensitivity to Detect Gravitational-Wave Events within our Galaxy
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations
• Setting upper limits on the strength of periodic gravitational waves using the first science data from the GEO600 and LIGO detectors
• 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
• Analysis of LIGO data for gravitational waves from binary neutron stars
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
• Hadamard Regularization
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild black hole -5.5 Post-Newtonian Formula-
• Equation of motion for relativistic compact binaries with the strong field point particle limit : the second and half post-Newtonian order
• The First Search for Gravitational Waves from Inspiraling Compact Binaries using TAMA300 data
• Binary black hole initial data for numerical general relativity based on post-Newtonian data
• Equation of motion for relativistic compact binaries with the strong field point particle limit : Formulation, the first post-Newtonian and multipole terms
• An approximate binary-black-hole metric
• Lorentzian regularization and the problem of point-like particles in general relativity
• Post-Newtonian Approximation
• Optimizing the third-and-a-half post-Newtonian gravitational radiation-reaction force for numerical simulations
• Time-symmetric initial data for binary black holes in numerical relativity
• Post-Newtonian Theory and its Application
• Coincidence analysis to search for inspiraling compact binaries

Cited by in corpus (61)

• Black holes, gravitational waves and fundamental physics: a roadmap
• 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
• Analytic black hole perturbation approach to gravitational radiation
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Transition from inspiral to plunge in precessing binaries of spinning black holes
• The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits
• Determination of Dark Energy by the Einstein Telescope: Comparing with CMB, BAO and SNIa Observations
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The non-spinning case
• 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
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses
• 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
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• 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
• Localization accuracy of compact binary coalescences detected by the third-generation gravitational-wave detectors and implication for cosmology
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction
• 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
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• A physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries
• Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Binary black hole spectroscopy
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Phenomenology of amplitude-corrected post-Newtonian gravitational waveforms for compact binary inspiral. I. Signal-to-noise ratios
• A quasi-physical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Testing Brans-Dicke gravity using the Einstein telescope
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• Gravitational-wave tail effects to quartic non-linear order
• Multi-messenger Detection Rates and distributions of Binary Neutron Star Mergers and Their Cosmological Implications
• Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
• Ineffectiveness of Padé resummation techniques in post-Newtonian approximations
• On the Circular Orbit Approximation for Binary Compact Objects In General Relativity
• Measuring the Hubble constant with coalescences of binary neutron star and neutron star-black hole: bright sirens \& dark sirens
• 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
• Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates
• On the origin of the notion of GW et cetera
• A New Template Family For The Detection Of Gravitational Waves From Comparable Mass Black Hole Binaries
• Analytic Approximations in GR and Gravitational Waves
• General Relativistic Dynamics of Compact Binary Systems
• Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies
• Equations of motion for compact binary systems in general relativity: Do they depend on the bodies' internal structure at the third post-Newtonian order?
• Two body dynamics in a quadratic modification of general relativity
• The Equivalence and/or the Effacing principle in $f\left(R\right)$ theories of gravity