Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes

Abstract

We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through $\mathcal{O}(G^3)$ to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a non-relativistic effective field theory. We also apply the Kosower-Maybee-O'Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.

6 pages + references + supplementary material, 1 figure

References in corpus (151)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
• 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
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Spin effects in the inspiral of coalescing compact binaries
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• General Relativity from Scattering Amplitudes
• A novel approach to integration by parts reduction
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Higher-order spin effects in the dynamics of compact binaries II. Radiation field
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Classical Space-Times from the S Matrix
• Testing gravity to second post-Newtonian order: a field-theory approach
• Radiation and the classical double copy for color charges
• Classical black hole scattering from a worldline quantum field theory
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• xTras: a field-theory inspired xAct package for Mathematica
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Observables and amplitudes for spinning particles and black holes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• The simplest massive S-matrix: from minimal coupling to Black Holes
• xPert: Computer algebra for metric perturbation theory
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Kerr Black Holes as Elementary Particles
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion
• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
• 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
• The double copy: Bremsstrahlung and accelerating black holes
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• On-shell heavy particle effective theories
• Degeneracy between mass and spin in black-hole-binary waveforms
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
• Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Gravitational Bremsstrahlung from Reverse Unitarity
• Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
• Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
• Gravitational spin Hamiltonians from the S matrix
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Heavy Black Hole Effective Theory
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Detecting binary neutron star systems with spin in advanced gravitational-wave detectors
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Gravitational Radiation from Color-Kinematics Duality
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• SUSY in the Sky with Gravitons
• Spinning particles, axion radiation, and the classical double copy
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• Tidal Effects in the Post-Minkowskian Expansion
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Static two-body potential at fifth post-Newtonian order
• Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order
• Spin-squared Hamiltonian of next-to-leading order gravitational interaction
• Bound states and the classical double copy
• Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form
• Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
• ADM canonical formalism for gravitating spinning objects
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Leading order finite size effects with spins for inspiralling compact binaries
• Compton Black-Hole Scattering for $s\le 5/2$
• Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Logarithmic Terms in the Soft Expansion in Four Dimensions
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Classical potential for general spinning bodies
• Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• A worldsheet for Kerr
• Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Non-conservative effects on Spinning Black Holes from World-Line Effective Field Theory
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Infrared features of gravitational scattering and radiation in the eikonal approach
• Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem
• Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Tidal effects in quantum field theory
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Mining the Geodesic Equation for Scattering Data
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Gravity Waves from Soft Theorem in General Dimensions
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries
• Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• Radiation reaction for spinning black-hole scattering
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• From Boundary Data to Bound States III: Radiative Effects
• NNNLO gravitational quadratic-in-spin interactions at the quartic order in G
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• On the Double Copy for Spinning Matter
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Tidal effects for spinning particles
• Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Strings, extended objects, and the classical double copy
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• NLO gravitational quartic-in-spin interaction
• Caravel: A C++ Framework for the Computation of Multi-Loop Amplitudes with Numerical Unitarity
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity
• A Classical Proof of the Classical Soft Graviton Theorem in D>4
• Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order
• Subleading Poles in the Numerical Unitarity Method at Two Loops
• The Two-Loop Four-Graviton Scattering Amplitudes
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics
• Hyperbolic scattering of spinning particles by a Kerr black hole
• Soft Radiation from Scattering Amplitudes Revisited
• Interplay of spin-precession and higher harmonics in the parameter estimation of binary black holes
• Gravitational waves from spinning binary black holes at the leading post-Newtonian orders at all orders in spin
• Classical Gravitational Self-Energy from Double Copy
• On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries
• Classical gravitational scattering from a gauge-invariant double copy

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• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Resummed spinning waveforms from five-point amplitudes
• Classical Spin Gravitational Compton Scattering
• Classical Limit of Higher-Spin String Amplitudes
• Spinning waveforms from KMOC at leading order
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Recursion in the classical limit and the neutron-star Compton amplitude
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• Boundary to bound dictionary for generic Kerr orbits
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• Observables from the Spinning Eikonal
• Gravitational Bound Waveforms from Amplitudes
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
• Large Gauge Effects and the Structure of Amplitudes
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Covariant actions and propagators for all spins, masses, and dimensions
• Charged test-particle scattering and effective one-body metrics with spin
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models
• Consistent actions for massive particles interacting with electromagnetism and gravity
• The first law of binary black hole scattering
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Loop corrections versus marginal deformation in celestial holography
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• Exploring gravitational impulse via quantum Boltzmann equation
• Double soft graviton factors from the gravitational Wilson line
• Gravitational multipoles from scattering amplitudes in higher dimensions
• Unexpected Symmetries of Kerr Black Hole Scattering