Classical Gravitational Observables from the Eikonal Operator

Abstract

We propose two possible eikonal operators encoding the effects of classical radiation as coherent states of gravitons and show how to compute from them different classical observables. In the first proposal, only genuinely propagating gravitons are included, while, in the second, zero-frequency modes are added in order to recover the effects of a static gravitational field. We first calculate the radiated energy-momentum and the change in each particle's momentum, or impulse, to 3PM order finding agreement with the literature. We then calculate the angular momentum of the gravitational field after the collision. In order to do so, we adapt the method of reverse unitarity to the presence of derivatives in the operators describing the angular momentum and reproduce the result of~\cite{Manohar:2022dea} obtained by resumming the small-velocity expansion. As a new application, we derive also the variation in each particle's angular momentum up to 3PM: calculating separately field and particle contributions allows us to check the balance laws explicitly. We also show how the eikonal operator encodes the linear-response formula of Bini-Damour by deriving the linear radiation-reaction contribution to the transverse impulse at 4PM.

22 pages

References in corpus (37)

• Higgs boson production at hadron colliders in NNLO QCD
• 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
• General Relativity from Scattering Amplitudes
• Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Radiation and the classical double copy for color charges
• Radiative contribution to classical gravitational scattering at the third order in $G$
• Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
• Universality of ultra-relativistic gravitational scattering
• Gravitational Bremsstrahlung from Reverse Unitarity
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Radiation Reaction from Soft Theorems
• Gravitational radiation reaction along general orbits in the effective one-body formalism
• Shaving off Black Hole Soft Hair
• On an Exponential Representation of the Gravitational S-Matrix
• Classical Gravity from Loop Amplitudes
• Radiative contributions to gravitational scattering
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Infrared features of gravitational scattering and radiation in the eikonal approach
• NLO Higgs boson rapidity distribution at hadron colliders
• BMS Supertranslation Symmetry Implies Faddeev-Kulish Amplitudes
• An $S$-Matrix for Massless Particles
• Unified limiting form of graviton radiation at extreme energies
• Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects
• Angular momentum of zero-frequency gravitons
• Self-force effects in post-Minkowskian scattering
• Soft gravitational radiation from ultra-relativistic collisions at sub- and sub-sub-leading order
• Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Coulombic contribution to the flux of angular momentum in general relativity
• A Supertranslation-Invariant Formula for the Angular Momentum Flux in Gravitational Scattering
• Electromagnetic Scoot
• The eikonal operator at arbitrary velocities I: the soft-radiation limit

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• Unified Treatment of null and Spatial Infinity IV: Angular Momentum at Null and Spatial Infinity
• Wave scattering event shapes at high energies
• Radiation eikonal for post-Minkowskian observables
• Dirac brackets for classical radiative observables
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Spinning waveforms of scalar radiation in quadratic modified gravity
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• On-shell approach to scalar hair in spinning binaries
• Double soft graviton factors from the gravitational Wilson line
• Frames and Slicings for Angular Momentum in Post-Minkowski Scattering