On Post-Minkowskian Hamiltonians in General Relativity

Abstract

We describe the computation of post-Minkowskian Hamiltonians in General Relativity from scattering amplitudes. Using a relativistic Lippmann-Schwinger equation, we relate perturbative amplitudes of massive scalars coupled to gravity to the post-Minkowskian Hamiltonians of classical General Relativity to any order in Newton's constant. We illustrate this by deriving an Hamiltonian for binary black holes without spin up to 2nd order in the post-Minkowskian expansion and demonstrate explicitly the equivalence with the recently proposed method based on an effective field theory matching.

17 pages. v2: minor corrections version to appear in Physical Review D

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Cited by in corpus (107)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Classical black hole scattering from a worldline quantum field theory
• 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
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Kerr Black Holes as Elementary Particles
• Radiative contribution to classical gravitational scattering at the third order in $G$
• On-shell heavy particle effective theories
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Gravitational Bremsstrahlung from Reverse Unitarity
• Radiation Reaction from Soft Theorems
• Heavy Black Hole Effective Theory
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• 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
• On an Exponential Representation of the Gravitational S-Matrix
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Mechanism for the quantum natured gravitons to entangle masses
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Compton Black-Hole Scattering for $s\le 5/2$
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Tidal effects in quantum field theory
• Classical Solutions and their Double Copy in Split Signature
• Classical observables from coherent-spin amplitudes
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Mining the Geodesic Equation for Scattering Data
• Classical Yang-Mills observables from amplitudes
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Kerr-Newman from Minimal Coupling
• Angular momentum of zero-frequency gravitons
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Gravitational shock waves and scattering amplitudes
• Infrared Divergences and the Eikonal Exponentiation
• Exponentiation of the leading eikonal with spin
• Scattering Angles in Kerr Metrics
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory
• Strings, extended objects, and the classical double copy
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• The Double Copy of Massive Scalar-QCD
• Classical Spin Gravitational Compton Scattering
• Horizon radiation reaction forces
• Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
• Recursion in the classical limit and the neutron-star Compton amplitude
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Bethe-Salpeter equation for classical gravitational bound states
• Light-ray operators, detectors and gravitational event shapes
• Observables from the Spinning Eikonal
• Soft Radiation from Scattering Amplitudes Revisited
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Distinguishing Jordan and Einstein frames in gravity through entanglement
• New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• 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
• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• The H-graph with equal masses in terms of multiple polylogarithms
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Gravitational decoherence by the apparatus in the quantum-gravity induced entanglement of masses
• A scattering amplitudes approach to hard thermal loops
• Charged test-particle scattering and effective one-body metrics with spin
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Minimal spin deflection of Kerr-Newman and Supersymmetric black hole
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Waveforms from Amplitudes
• Relativistic Dips in Entangling Power of Gravity
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• General Relativity from Intersection Theory
• Machine Learning Post-Minkowskian Integrals
• Fixing the non-relativistic expansion of the 1PM potential
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Probing the post-Minkowskian approximation using recursive addition of self-interactions
• The hierarchical three-body problem at $\mathcal{O}(G^2)$
• The Radial Action from Probe Amplitudes to All Orders
• Yang-Mills observables: from KMOC to eikonal through EFT
• Scattering Amplitudes for Binary Systems beyond GR
• NS-NS Spacetimes from Amplitudes
• Unexpected Symmetries of Kerr Black Hole Scattering
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework