Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$

Abstract

We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin $S$. By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the $\mathcal{O}(G^2)$ quadratic-in-spin two-body Hamiltonian. We first evaluate the $S^3$ scattering angle and two-body Hamiltonian at this order in $G$, including not only all operators corresponding to the usual worldline operators, but also an additional set due to an interesting subtlety. We then evaluate $S^4$ and $S^5$ contributions at $\mathcal{O}(G^2)$ which we confirm by comparing against aligned-spin results. We conjecture that a certain shift symmetry together with a constraint on the high-energy growth of the scattering amplitude specify the Wilson coefficients for the Kerr black hole to all orders in the spin and confirm that they reproduce the previously-obtained results through $S^4$.

arXiv comment8 pages and ancillary files; v2: references added; typos corrected; presentation improved; v3: accepted for publication; additional data on aligned-spin scattering angles included as ancillary files

References in corpus (111)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• General relativity as an effective field theory: The leading quantum corrections
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Algorithm FIRE -- Feynman Integral REduction
• 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
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• 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
• Direct extraction of one-loop integral coefficients
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• 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
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• 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
• 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
• On-shell Techniques and Universal Results in Quantum Gravity
• Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries
• 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
• On Post-Minkowskian Hamiltonians in General Relativity
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• On-shell heavy particle effective theories
• 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
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• 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
• Heavy Black Hole Effective Theory
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Direct Extraction Of One Loop Rational Terms
• 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
• Tidal Effects in the Post-Minkowskian Expansion
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Spin-squared Hamiltonian of next-to-leading order gravitational interaction
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
• The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form
• ADM canonical formalism for gravitating spinning objects
• Radiative contributions to gravitational scattering
• 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
• 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
• Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme
• Classical potential for general spinning bodies
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme
• Tidal effects in quantum field theory
• Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Mining the Geodesic Equation for Scattering Data
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• Test black holes, scattering amplitudes and perturbations of Kerr spacetime
• Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields
• NNNLO gravitational quadratic-in-spin interactions at the quartic order in G
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Tidal effects for spinning particles
• A Bound on Massive Higher Spin Particles
• NLO gravitational quartic-in-spin interaction
• Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order
• Consistent Non-Minimal Couplings of Massive Higher-Spin Particles
• Soft Matters, or the Recursions with Massive Spinors
• Hyperbolic scattering of spinning particles by a Kerr black hole
• A cautionary case of casual causality
• Massive Higher Spin States in String Theory and the Principle of Equivalence
• Simplifying $D$-Dimensional Physical-State Sums in Gauge Theory and Gravity
• Gravitational waves from spinning binary black holes at the leading post-Newtonian orders at all orders in spin
• 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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• Classical Limit of Higher-Spin String Amplitudes
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• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• 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
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• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• Large Gauge Effects and the Structure of Amplitudes
• Massive twistor worldline in electromagnetic fields
• From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance at the 4.5PN Precision Frontier
• 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
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Consistent actions for massive particles interacting with electromagnetism and gravity
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Loop corrections versus marginal deformation in celestial holography
• Unexpected Symmetries of Kerr Black Hole Scattering
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• Gravitational multipoles from scattering amplitudes in higher dimensions