Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach

Abstract

We present the contribution from potential interactions to the dynamics of non-spinning binaries to fourth Post-Minkowskian (4PM) order. This is achieved by computing the scattering angle to $\mathcal{O}(G^4)$ using the effective field theory approach and deriving the bound radial action through analytic continuation. We reconstruct the Hamiltonian and center-of-mass momentum in an isotropic gauge. The (three-loop) integrals involved in our calculation are computed via differential equations, including a sector yielding elliptic integrals. Using the universal link between potential and tail terms, we also report: 1) The instantaneous energy flux at $\mathcal{O}(G^3)$; 2) The contribution to the 4PM unbound/bound radial action(s) depending on logarithms of the binding energy; 3) The (scheme-independent) logarithmic contribution to the 4PM non-local tail Hamiltonian for circular orbits. Our results in the potential region are in agreement with the recent derivation from scattering amplitudes. We also find perfect agreement in the overlap with the state-of-the-art in Post-Newtonian theory.

arXiv comment9 pages, 1 figure. 1 ancillary file (txt format). v2: Published version

References in corpus (62)

• Laser Interferometer Space Antenna
• Multiloop integrals in dimensional regularization made simple
• An Effective Field Theory of Gravity for Extended Objects
• Differential Equations for Feynman Graph Amplitudes
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• The Effective Field Theorist's Approach to Gravitational Dynamics
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Prospects for Fundamental Physics with LISA
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Classical Space-Times from the S Matrix
• Radiation and the classical double copy for color charges
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Observables and amplitudes for spinning particles and black holes
• Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries
• Reducing differential equations for multiloop master integrals
• 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
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Gravitational spin Hamiltonians from the S matrix
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• The Tune of Love and the Nature(ness) of Spacetime
• Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
• Effective field theory methods to model compact binaries
• Absorption Effects due to Spin in the Worldline Approach to Black Hole Dynamics
• Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order
• Tidal Effects in the Post-Minkowskian Expansion
• Static two-body potential at fifth post-Newtonian order
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• epsilon: A tool to find a canonical basis of master integrals
• Bound states and the classical double copy
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Radiation reaction and gravitational waves in the effective field theory approach
• Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order
• 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
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Multipole expansion at the level of the action
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• Tidal effects in quantum field theory
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• How to choose master integrals
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• Logarithmic tail contributions to the energy function of circular compact binaries
• Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach
• The Lamb shift and the gravitational binding energy for binary black holes
• Next-to-leading order spin-orbit effects in the equations of motion, energy loss and phase evolution of binaries of compact bodies in the effective field theory approach
• Classical gravitational scattering from a gauge-invariant double copy

Cited by in corpus (83)

• 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
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Radiative contributions to gravitational scattering
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• The Science of the Einstein Telescope
• The Sub-Leading Scattering Waveform from Amplitudes
• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Resummed spinning waveforms from five-point amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• From Boundary Data to Bound States III: Radiative Effects
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects
• Effective Field Theory for Extreme Mass Ratios
• Scattering Angles in Kerr Metrics
• Self-force effects in post-Minkowskian scattering
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Strong-field scattering of two spinning black holes: Numerics versus Analytics
• Classical Spin Gravitational Compton Scattering
• Spinning waveforms from KMOC at leading order
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Unveiling the merger structure of black hole binaries in generic planar orbits
• Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
• Recursion in the classical limit and the neutron-star Compton amplitude
• Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Observables from the Spinning Eikonal
• Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Scattering and dynamical capture of two black holes: synergies between numerical and analytical methods
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• Self-consistent Effective-one-body theory for spinless binaries based on post-Minkowskian approximation I: Hamiltonian and decoupled equation for ${\psi }_4^B$
• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Binary Dynamics from Worldline QFT for Scalar-QED
• Calabi-Yau Feynman integrals in gravity: $\epsilon$-factorized form for apparent singularities
• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• Large Gauge Effects and the Structure of Amplitudes
• Gravitational radiation contributions to the two-body scattering angle
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Frequency-domain approach to self-force in hyperbolic scattering
• Electromagnetic Scoot
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Binary systems in massive scalar-tensor theories: Next-to-leading order gravitational wave phase from effective field theory
• Radiation eikonal for post-Minkowskian observables
• Charged test-particle scattering and effective one-body metrics with spin
• Conservative Scattering of Reissner-Nordström Black Holes at Third Post-Minkowskian Order
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Effective metric of spinless binaries with radiation-reaction effect up to fourth Post-Minkowskian order in effective-one-body theory
• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• General Relativity from Intersection Theory
• Testing the Boundary-to-Bound Correspondence with Numerical Relativity
• Machine Learning Post-Minkowskian Integrals
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• Tidal Love Numbers of Neutron Stars in Horndeski Theories
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Strong Field Scattering of Two Black Holes: Exploring Gauge Flexibility
• Dynamics for Super-Extremal Kerr Binary Systems at $\mathcal{O}(G^2)$
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• The spectrum of Feynman-integral geometries at two loops
• Double soft graviton factors from the gravitational Wilson line
• The Radial Action from Probe Amplitudes to All Orders
• Scattering Amplitudes for Binary Systems beyond GR
• Exploring gravitational impulse via quantum Boltzmann equation
• Unexpected Symmetries of Kerr Black Hole Scattering
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework