Sixth post-Newtonian nonlocal-in-time dynamics of binary systems

Abstract

We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary nonlocal-in-time dynamics. On the one hand, we compute the nonlocal part of the scattering angle for hyberboliclike motions; and, on the other hand, we compute the nonlocal part of the averaged (Delaunay) Hamiltonian for ellipticlike motions. The former is computed as a large-angular-momentum expansion (given here to next-to-next-to-leading order), while the latter is given as a small-eccentricity expansion (given here to the tenth order). We note the appearance of $\zeta (3)$ in the nonlocal part of the scattering angle. The averaged Hamiltonian for ellipticlike motions then yields two more gauge-invariant observables: the energy and the periastron precession as functions of orbital frequencies. We point out the existence of a hidden simplicity in the mass-ratio dependence of the gravitational-wave energy loss of a two-body system.

59 pages, no figures, one ancillary text file

References in corpus (14)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Fourth post-Newtonian effective one-body dynamics
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Static two-body potential at fifth post-Newtonian order
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• 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
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Eikonal Scattering in Kaluza-Klein Gravity

Cited by in corpus (70)

• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Gravitational Bremsstrahlung from Reverse Unitarity
• Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes
• 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
• Radiative contributions to gravitational scattering
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• The Science of the Einstein Telescope
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Effective-one-body waveforms from dynamical captures in black hole binaries
• Enhancing the SEOBNRv5 effective-one-body waveform model with second-order gravitational self-force fluxes
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Emergence of Calabi-Yau manifolds in high-precision black hole scattering
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory
• 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
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• 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
• 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
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• 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
• Spinning waveforms from KMOC at leading order
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Tail contributions to gravitational conservative dynamics
• Inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity within the effective-one-body formalism
• Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity
• Boundary to bound dictionary for generic Kerr orbits
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Gravitational Bound Waveforms from Amplitudes
• Higher-order tail contributions to the energy and angular momentum fluxes in a two-body scattering process
• Efficient resummation of high post-Newtonian contributions to the binding energy
• Binary Dynamics from Worldline QFT for Scalar-QED
• Gravitational radiation contributions to the two-body scattering angle
• Effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order
• Charged test-particle scattering and effective one-body metrics with spin
• Third post-Newtonian gravitational radiation from two-body scattering II. Hereditary Energy radiation
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Waveforms from Amplitudes
• Can Two Ultrarelativistic Objects Lose Almost All Their Energy to Gravitational Radiation?
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Machine Learning Post-Minkowskian Integrals
• Momentum recoil in the relativistic two-body problem: higher-order tails
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation
• Strong Field Scattering of Two Black Holes: Exploring Gauge Flexibility
• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order
• Frequency domain analysis of the gravitational wave energy loss in hyperbolic encounters
• Compact binary system dynamics at the second post-Newtonian order: analytical formula of the coordinate time for eccentric and circular orbits
• First-post-Newtonian generation of gravitational waves in Einstein-Cartan theory
• The Radial Action from Probe Amplitudes to All Orders
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework