Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach

Abstract

We calculate the motion of binary mass systems in gravity up to the fourth post--Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying dimensional regularization. We construct the canonical transformations to ADM coordinates and to effective one body theory (EOB) to compare with other approaches. We show that intermediate poles in the dimensional regularization parameter $\epsilon$ vanish in the observables and the classical theory is not renormalized. The results are illustrated for a series of observables for which we agree with the literature.

28 pages, 2 Figures

References in corpus (10)

• 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
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Effective field theory calculation of second post-Newtonian binary dynamics
• Static two-body potential at fifth post-Newtonian order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

Cited by in corpus (59)

• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• 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
• Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections
• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• The Science of the Einstein Telescope
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Mining the Geodesic Equation for Scattering Data
• Resummed spinning waveforms from five-point amplitudes
• Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Tail contributions to gravitational conservative dynamics
• Gravitational-wave tails of memory
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• Fourth post-Newtonian effective-one-body Hamiltonians with generic spins
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies
• 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
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• The H-graph with equal masses in terms of multiple polylogarithms
• Conservative (failed)-tail effects at the fifth post-Newtonian order
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Parametrized multipolar gravitational waveforms for testing general relativity: Amplitude corrections up to 2PN order
• Classical gravitational scattering from a gauge-invariant double copy
• Scrambling and Entangling Spinning Particles
• Tests of general relativity at the fourth post-Newtonian order
• Two-body problem in curved spacetime: exploring gravitational wave transient cases
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
• Hamiltonian normal forms for the post-Newtonian binary problem