Post-Minkowskian Scattering Angle in Einstein Gravity

Abstract

Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential. All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion.

24 pages, minor corrections, published version to appear in JHEP

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Cited by in corpus (68)

• 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
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Radiative contribution to classical gravitational scattering at the third order in $G$
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• 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
• On an Exponential Representation of the Gravitational S-Matrix
• Radiative contributions to gravitational scattering
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Compton Black-Hole Scattering for $s\le 5/2$
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• A worldsheet for Kerr
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Tidal effects in quantum field theory
• Classical Solutions and their Double Copy in Split Signature
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Mining the Geodesic Equation for Scattering Data
• Classical Yang-Mills observables from amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects
• Tidal effects for spinning particles
• Angular momentum of zero-frequency gravitons
• Infrared Divergences and the Eikonal Exponentiation
• Gravitational shock waves and scattering amplitudes
• Exponentiation of the leading eikonal with spin
• Scattering Angles in Kerr Metrics
• Horizon radiation reaction forces
• Recursion in the classical limit and the neutron-star Compton amplitude
• Bethe-Salpeter equation for classical gravitational bound states
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• Light-ray operators, detectors and gravitational event shapes
• Observables from the Spinning Eikonal
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• 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
• Large Gauge Effects and the Structure of Amplitudes
• The Reissner-Nordström-Tangherlini solution from scattering amplitudes of charged scalars
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Charged test-particle scattering and effective one-body metrics with spin
• Conservative Scattering of Reissner-Nordström Black Holes at Third Post-Minkowskian Order
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Minimal spin deflection of Kerr-Newman and Supersymmetric black hole
• Waveforms from Amplitudes
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• Fixing the non-relativistic expansion of the 1PM potential
• Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation
• The Radial Action from Probe Amplitudes to All Orders
• Yang-Mills observables: from KMOC to eikonal through EFT
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• Unexpected Symmetries of Kerr Black Hole Scattering
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order