Radiative contributions to gravitational scattering

Abstract

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in General Relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to non-trivial identities relating the various radiative losses. At order $G^3$ our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order $G^4$ we compute the needed radiative losses to next-to-next-to-leading-order in the post-Newtonian expansion, thereby reaching the absolute fourth and a half post-Newtonian level of accuracy in the 4-momentum changes. We also provide explicit expressions, at the absolute sixth post-Newtonian accuracy, for the radiation-graviton contribution to {\it conservative} $O(G^4)$ scattering. At orders $G^5$ and $G^6$ we derive explicit theoretical expressions for the last two hitherto undetermined parameters describing the fifth-post-Newtonian dynamics. Our results at the fifth-post-Newtonian level confirm results of [Nucl. Phys. B \textbf{965}, 115352 (2021)] but exhibit some disagreements with results of [Phys. Rev. D \textbf{101}, 064033 (2020)].

46 pages; revtex macros used. V2: References added. V3: Minor changes in the text. V4: Corrected Eqs. 9.9-9.11 by overall signs, corrected Eq. 9.45 and consequent adjustment of related results; Conclusions unchanged

References in corpus (19)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body 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
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• The current-type quadrupole moment and gravitational-wave mode $(\ell ,m)=(2,1)$ of compact binary systems at the third post-Newtonian order
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• Near and far zone in two-body dynamics: an effective field theory perspective
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order
• Canonical center and relative coordinates for compact binary systems through second post-Newtonian order

Cited by in corpus (39)

• Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
• SUSY in the Sky with Gravitons
• On an Exponential Representation of the Gravitational S-Matrix
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• 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
• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Classical Gravitational Observables from the Eikonal Operator
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Radiation reaction for spinning black-hole scattering
• Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• 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
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• 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
• Tail contributions to gravitational conservative dynamics
• Graviton particle statistics and coherent states from classical scattering amplitudes
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Radiation-reaction and angular momentum loss at the second Post-Minkowskian order
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Higher-order tail contributions to the energy and angular momentum fluxes in a two-body scattering process
• Gravitational radiation contributions to the two-body scattering angle
• Third order post-Newtonian gravitational radiation from two-body scattering: Instantaneous energy and angular momentum radiation
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Can Two Ultrarelativistic Objects Lose Almost All Their Energy to Gravitational Radiation?
• Machine Learning Post-Minkowskian Integrals
• Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation
• The Radial Action from Probe Amplitudes to All Orders
• Frequency domain analysis of the gravitational wave energy loss in hyperbolic encounters
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order