The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant

Abstract

We derive the conservative part of the Lagrangian and the energy of a gravitationally bound two-body system at fourth post-Newtonian order, up to terms quadratic in the Newton constant. We also show that such terms are compatible with Lorentz invariance and we write an ansatz for the center-of-mass position. The remaining terms carrying higher powers of the Newton constant are currently under investigation.

arXiv comment24 pages, 2 figures. Typos in formulae corrected, references added, more comments in the conclusion in v2

References in corpus (33)

• An Effective Field Theory of Gravity for Extended Objects
• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• Dimensional regularization of the gravitational interaction of point masses
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries
• Gravitational radiative corrections from effective field theory
• Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion
• Dissipative Effects in the Worldline Approach to Black Hole Dynamics
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• 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
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Effective field theory calculation of second post-Newtonian binary dynamics
• Absorption Effects due to Spin in the Worldline Approach to Black Hole Dynamics
• Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
• Classical Effective Field Theory and Caged Black Holes
• Tail terms in gravitational radiation reaction via effective field theory
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Lorentzian regularization and the problem of point-like particles in general relativity
• Reliability of complete gravitational waveform models for compact binary coalescences
• The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory
• Einstein's action and the harmonic gauge in terms of Newtonian fields

Cited by in corpus (89)

• New Developments in FeynCalc 9.0
• Black holes, gravitational waves and fundamental physics: a roadmap
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Probing Ultralight Bosons with Binary Black Holes
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Classical Space-Times from the S Matrix
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• Fourth post-Newtonian effective one-body dynamics
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• The Tune of Love and the Nature(ness) of Spacetime
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Effective field theory methods to model compact binaries
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order
• Static two-body potential at fifth post-Newtonian order
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian
• The Science of the Einstein Telescope
• 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
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Dynamics of compact binary systems in scalar-tensor theories: I. Equations of motion to the third post-Newtonian order
• Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Resummed spinning waveforms from five-point amplitudes
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• On higher-derivative effects on the gravitational potential and particle bending
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• From Boundary Data to Bound States III: Radiative Effects
• Gravitational-wave tail effects to quartic non-linear order
• Logarithmic tail contributions to the energy function of circular compact binaries
• On the four-loop static contribution to the gravitational interaction potential of two point masses
• EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Gravitating binaries at 5PN in the post-Minkowskian approximation
• Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion
• The General Relativistic Two Body Problem and the Effective One Body Formalism
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• Equations of motion of self-gravitating $N$-body systems in the first post-Minkowskian approximation
• The Lamb shift and the gravitational binding energy for binary black holes
• Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
• Near and far zone in two-body dynamics: an effective field theory perspective
• Theory of post-Newtonian radiation and reaction
• Analyzing Gravitational Waves with General Relativity
• Efficient resummation of high post-Newtonian contributions to the binding energy
• Radiation Reaction for Non-Spinning Bodies at 4.5PN in the Effective Field Theory Approach
• Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order
• Conservative (failed)-tail effects at the fifth post-Newtonian order
• Analytic approximations, perturbation theory, effective field theory methods and their applications
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Classical 3-loop 2-body diagrams
• Half-solution to the two-body problem in General Relativity
• Testing the Boundary-to-Bound Correspondence with Numerical Relativity
• Analytic Approximations in GR and Gravitational Waves
• Machine Learning Post-Minkowskian Integrals
• The general relativistic two body problem
• Classical gravitational scattering from a gauge-invariant double copy
• Effects of Short-Distance Modifications to General Relativity in Spinning Binary Systems
• Post-newtonian analysis of precessing convention for spinning compact binaries
• Tests of general relativity at the fourth post-Newtonian order
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
• Exploring gravitational impulse via quantum Boltzmann equation
• Calculating the static gravitational two-body potential to fifth post-Newtonian order with Feynman diagrams