From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion

Abstract

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.

arXiv comment5 pages + references. v2: published version, minor corrections

References in corpus (29)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• New Relations for Gauge-Theory Amplitudes
• Asymptotic expansion of Feynman integrals near threshold
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• An Effective Field Theory of Gravity for Extended Objects
• Gravity as the Square of Gauge Theory
• Black holes and the double copy
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Classical Space-Times from the S Matrix
• Radiation and the classical double copy for color charges
• On-shell Techniques and Universal Results in Quantum Gravity
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Gravitational spin Hamiltonians from the S matrix
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Basics of Generalized Unitarity
• Effective field theory calculation of second post-Newtonian binary dynamics
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• The QCD heavy-quark potential to order v^2: one loop matching conditions
• Gravitating binaries at 5PN in the post-Minkowskian approximation

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• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• 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
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Observables and amplitudes for spinning particles and black holes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Classical and quantum scattering in post-Minkowskian gravity
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Kerr Black Holes as Elementary Particles
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• On Post-Minkowskian Hamiltonians in General Relativity
• Radiative contribution to classical gravitational scattering at the third order in $G$
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• On-shell heavy particle effective theories
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• 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
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Universality of ultra-relativistic gravitational scattering
• Gravitational Bremsstrahlung from Reverse Unitarity
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Radiation Reaction from Soft Theorems
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Heavy Black Hole Effective Theory
• Double copy for massive quantum particles with spin
• Sixth post-Newtonian local-in-time dynamics of binary systems
• 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
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• SUSY in the Sky with Gravitons
• Tidal Effects in the Post-Minkowskian Expansion
• Universality in the classical limit of massless gravitational scattering
• Static two-body potential at fifth post-Newtonian order
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• On an Exponential Representation of the Gravitational S-Matrix
• Classical Gravity from Loop Amplitudes
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Radiative contributions to gravitational scattering
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• 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
• Compton Black-Hole Scattering for $s\le 5/2$
• A Twistorial Foundation for the Classical Double Copy
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Classical potential for general spinning bodies
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• A worldsheet for Kerr
• The Sub-Leading Scattering Waveform from Amplitudes
• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• 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
• Tidal effects in quantum field theory
• Classical Solutions and their Double Copy in Split Signature
• Double Copy from Homotopy Algebras
• Topology and Wilson lines: global aspects of the double copy
• Integrability of Black Hole Orbits in Maximal Supergravity
• The classical double copy of non-singular black holes
• Classical observables from coherent-spin amplitudes
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Mining the Geodesic Equation for Scattering Data
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Classical Yang-Mills observables from amplitudes
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity 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
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• Radiation reaction for spinning black-hole scattering
• Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• Test black holes, scattering amplitudes and perturbations of Kerr spacetime
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Classical and quantum double copy of back-reaction
• From Boundary Data to Bound States III: Radiative Effects
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• NNNLO gravitational quadratic-in-spin interactions at the quartic order in G
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• The Newman-Penrose Map and the Classical Double Copy
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Kerr-Newman from Minimal Coupling
• On the Double Copy for Spinning Matter
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects
• Angular momentum of zero-frequency gravitons
• Tidal effects for spinning particles
• Classical Double Copy of Worldline Quantum Field Theory
• Monopoles, shockwaves and the classical double copy
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Effective Field Theory for Extreme Mass Ratios
• Gravitational shock waves and scattering amplitudes
• Infrared Divergences and the Eikonal Exponentiation
• Self-force effects in post-Minkowskian scattering
• Scattering Angles in Kerr Metrics
• Biadjoint wires
• Exponentiation of the leading eikonal with spin
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Strings, extended objects, and the classical double copy
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• New heavenly double copies
• Massive Gravity from Double Copy
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Classical Spin Gravitational Compton Scattering
• Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity
• Generalizations of the Double-Copy: the KLT Bootstrap
• Horizon radiation reaction forces
• Loop-Level Double-Copy for Massive Quantum Particles
• Rotating Black Holes in Cubic Gravity
• Gravitational Faraday effect from on-shell amplitudes
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Scattering of gravitational waves off spinning compact objects with an effective worldline theory
• Recursion in the classical limit and the neutron-star Compton amplitude
• Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
• The Two-Loop Four-Graviton Scattering Amplitudes
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Amplitude bases in generic EFTs
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Black Holes in Klein Space
• Bethe-Salpeter equation for classical gravitational bound states
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Boundary to bound dictionary for generic Kerr orbits
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• All order gravitational waveforms from scattering amplitudes
• Observables from the Spinning Eikonal
• Soft Radiation from Scattering Amplitudes Revisited
• Gauge $\times$ Gauge on Spheres
• Light-ray operators, detectors and gravitational event shapes
• Isometries and the double copy
• Classical resummation and breakdown of strong-field QED
• Radiation-reaction and angular momentum loss at the second Post-Minkowskian order
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Gravitational Bound Waveforms from Amplitudes
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Scalar-Graviton Amplitudes
• New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation
• Non-perturbative Double Copy in Flatland
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Classical and quantum gravitational scattering with Generalized Wilson Lines
• 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
• Efficient resummation of high post-Newtonian contributions to the binding energy
• Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation
• Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order
• Binary Dynamics from Worldline QFT for Scalar-QED
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Soft graviton exchange and the information paradox
• Extracting Einstein from the Loop-Level Double-Copy
• Large Gauge Effects and the Structure of Amplitudes
• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• Gluon helicity flip in a plane wave background
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• Virtues of a symmetric-structure double copy
• A tale of tails through generalized unitarity
• Post-Minkowskian Hamiltonians in Modified Theories of Gravity
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Frequency-domain approach to self-force in hyperbolic scattering
• Quantum corrections to frame-dragging in scattering amplitudes
• The Reissner-Nordström-Tangherlini solution from scattering amplitudes of charged scalars
• The H-graph with equal masses in terms of multiple polylogarithms
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• A scattering amplitudes approach to hard thermal loops
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Charged test-particle scattering and effective one-body metrics with spin
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Visions in Quantum Gravity
• 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
• Minimal spin deflection of Kerr-Newman and Supersymmetric black hole
• Half-solution to the two-body problem in General Relativity
• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• Waveforms from Amplitudes
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Spinning waveforms of scalar radiation in quadratic modified gravity
• Testing the Boundary-to-Bound Correspondence with Numerical Relativity
• General Relativity from Intersection Theory
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Machine Learning Post-Minkowskian Integrals
• Fixing the non-relativistic expansion of the 1PM potential
• Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity
• Momentum recoil in the relativistic two-body problem: higher-order tails
• The first law of binary black hole scattering
• New framework for classical double copies
• Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory
• The Weyl double copy from twistor space
• Scrambling and Entangling Spinning Particles
• The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Dynamics for Super-Extremal Kerr Binary Systems at $\mathcal{O}(G^2)$
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Strong Field Scattering of Two Black Holes: Exploring Gauge Flexibility
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation
• Probing the post-Minkowskian approximation using recursive addition of self-interactions
• On-shell approach to scalar hair in spinning binaries
• The Eikonal Approximation and the Gravitational Dynamics of Binary Systems
• Loop corrections versus marginal deformation in celestial holography
• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order
• Exploring gravitational impulse via quantum Boltzmann equation
• Yang-Mills observables: from KMOC to eikonal through EFT
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
• Quantum point particle approximation of spinning black holes and compact stars
• Scattering Amplitudes for Binary Systems beyond GR
• The Radial Action from Probe Amplitudes to All Orders
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
• General Relativity from Quantum Field Theory
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• Notes on AdS-Schwarzschild eikonal phase
• NS-NS Spacetimes from Amplitudes
• On-Shell Perspectives on the Massless Limit of Massive Supergravity
• Unexpected Symmetries of Kerr Black Hole Scattering
• Testing gravity with the two-body problem