From Boundary Data to Bound States

Abstract

We introduce a -- somewhat holographic -- dictionary between gravitational observables for scattering processes (measured at the "boundary") and adiabatic invariants for bound orbits (in the "bulk"), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the two-body problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance $\Delta \Phi$) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, $\Omega (E)$, directly from scattering information. As an example, using the results in Bern et al. [1901.04424, 1908.01493], we readily derive $\Omega (E)$ and $\Delta \Phi (J,E)$ to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a "no-recoil" approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.

51 pages. 3 Figures. v4 Published version

References in corpus (57)

• Multi-messenger Observations of a Binary Neutron Star Merger
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Asymptotic expansion of Feynman integrals near threshold
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• The Effective Field Theorist's Approach to Gravitational Dynamics
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Black holes and the double copy
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• High-energy gravitational scattering and the general relativistic two-body problem
• 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
• Classical Space-Times from the S Matrix
• Observables and amplitudes for spinning particles and black holes
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• A Highly Spinning and Aligned Binary Black Hole Merger in the Advanced LIGO First Observing Run
• Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion
• On Post-Minkowskian Hamiltonians in General Relativity
• Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• 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
• Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
• Novel approach to binary dynamics: application to the fifth post-Newtonian level
• Gravitational spin Hamiltonians from the S matrix
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Double copy for massive quantum particles with spin
• 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
• Effective field theory methods to model compact binaries
• Absorption Effects due to Spin in the Worldline Approach to Black Hole Dynamics
• 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
• Bound states and the classical double copy
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Integrability of Black Hole Orbits in Maximal Supergravity
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• 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
• Spin-multipole effects in binary black holes and the test-body limit
• Gravitating binaries at 5PN in the post-Minkowskian approximation
• Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion
• The Lamb shift and the gravitational binding energy for binary black holes
• Generating exact solutions to Einstein's equation using linearized approximations

Cited by in corpus (154)

• 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 black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Classical and quantum scattering in post-Minkowskian gravity
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Radiative contribution to classical gravitational scattering at the third order in $G$
• On-shell heavy particle effective theories
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• 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
• Gravitational Bremsstrahlung from Reverse Unitarity
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• 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
• 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
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Compton Black-Hole Scattering for $s\le 5/2$
• A Twistorial Foundation for the Classical Double Copy
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• The Science of the Einstein Telescope
• A worldsheet for Kerr
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• 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
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Tidal effects in quantum field theory
• Classical Solutions and their Double Copy in Split Signature
• Classical observables from coherent-spin amplitudes
• Emergence of Calabi-Yau manifolds in high-precision black hole scattering
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Mining the Geodesic Equation for Scattering Data
• The Classical Double Copy of a Point Charge
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Classical Yang-Mills observables from amplitudes
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• 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
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Tidal effects for spinning particles
• Angular momentum of zero-frequency gravitons
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Effective Field Theory for Extreme Mass Ratios
• Infrared Divergences and the Eikonal Exponentiation
• Gravitational shock waves and scattering amplitudes
• Self-force effects in post-Minkowskian scattering
• Scattering Angles in Kerr Metrics
• 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
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• The Double Copy of Massive Scalar-QCD
• Horizon radiation reaction forces
• Rotating Black Holes in Cubic Gravity
• Spinning waveforms from KMOC at leading order
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Unveiling the merger structure of black hole binaries in generic planar orbits
• Scattering of gravitational waves off spinning compact objects with an effective worldline theory
• 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
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Black Holes in Klein Space
• Bethe-Salpeter equation for classical gravitational bound states
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• 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
• Geodesics From Classical Double Copy
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• Isometries and the double copy
• Light-ray operators, detectors and gravitational event shapes
• Soft Radiation from Scattering Amplitudes Revisited
• Gravitational Bound Waveforms from Amplitudes
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• Turning black-holes and D-branes inside out their photon-spheres
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Efficient resummation of high post-Newtonian contributions to the binding energy
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Calabi-Yau Feynman integrals in gravity: $\epsilon$-factorized form for apparent singularities
• Time-domain metric reconstruction for hyperbolic scattering
• Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• Massive twistor worldline in electromagnetic fields
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Frequency-domain approach to self-force in hyperbolic scattering
• 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
• Quantization Conditions and the Double Copy
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• Third post-Newtonian gravitational radiation from two-body scattering II. Hereditary Energy radiation
• Dirac brackets for classical radiative observables
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• 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
• Bound States of the Schwarzschild Black Hole
• Minimal spin deflection of Kerr-Newman and Supersymmetric black hole
• Half-solution to the two-body problem in General Relativity
• Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models
• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• Waveforms from Amplitudes
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Testing the Boundary-to-Bound Correspondence with Numerical Relativity
• 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
• Machine Learning Post-Minkowskian Integrals
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• The first law of binary black hole scattering
• The Weyl double copy from twistor space
• Relieving scale disparity in binary black hole simulations
• Black-hole scattering with numerical relativity: Self-force extraction and post-Minkowskian validation
• Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation
• Strong Field Scattering of Two Black Holes: Exploring Gauge Flexibility
• On-shell approach to scalar hair in spinning binaries
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• The Radial Action from Probe Amplitudes to All Orders
• Double soft graviton factors from the gravitational Wilson line
• Yang-Mills observables: from KMOC to eikonal through EFT
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• NS-NS Spacetimes from Amplitudes
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order