Leading Nonlinear Tidal Effects and Scattering Amplitudes

Abstract

We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections.

arXiv comment45 pages, 7 figures

References in corpus (118)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Effective one-body approach to general relativistic two-body dynamics
• General relativity as an effective field theory: The leading quantum corrections
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Constraining neutron star tidal Love numbers with gravitational wave detectors
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Differential Equations for Two-Loop Four-Point Functions
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Relativistic tidal properties of neutron stars
• Transition from inspiral to plunge in binary black hole coalescences
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Relativistic theory of tidal Love numbers
• Black holes, gravitational waves and fundamental physics: a roadmap
• An Effective Field Theory of Gravity for Extended Objects
• Differential Equations for Feynman Graph Amplitudes
• Dimensionally Regulated Pentagon Integrals
• Gravitational Radiation Reaction to a Particle Motion
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Algorithm FIRE -- Feynman Integral REduction
• One-Loop Amplitudes for e^+ e^- to Four Partons
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• The Effective Field Theorist's Approach to Gravitational Dynamics
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Self-force and radiation reaction in general relativity
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Massive Loop Amplitudes from Unitarity
• High-energy gravitational scattering and the general relativistic two-body problem
• Dimensional regularization of the gravitational interaction of point masses
• General Relativity from Scattering Amplitudes
• Testing strong-field gravity with tidal Love numbers
• Counting Gauge Invariants: the Plethystic Program
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian
• Neutron star tidal deformability and equation of state constraints
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Classical Space-Times from the S Matrix
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• 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
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• No-hair theorem for Black Holes in Astrophysical Environments
• On-shell Techniques and Universal Results in Quantum Gravity
• Black hole stereotyping: Induced gravito-static polarization
• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
• A Gravitational Wave Detector with Cosmological Reach
• On Post-Minkowskian Hamiltonians in General Relativity
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Distinguishing Boson Stars from Black Holes and Neutron Stars from Tidal Interactions in Inspiraling Binary Systems
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Dark halos around neutron stars and gravitational waves
• Novel approach to binary dynamics: application to the fifth post-Newtonian level
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• An effective formalism for testing extensions to General Relativity with gravitational waves
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• 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
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Classical Physics and Quantum Loops
• Static response and Love numbers of Schwarzschild black holes
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Effective field theory calculation of second post-Newtonian binary dynamics
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order
• Tidal Effects in the Post-Minkowskian Expansion
• Universality in the classical limit of massless gravitational scattering
• Static two-body potential at fifth post-Newtonian order
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
• Classical Effective Field Theory and Caged Black Holes
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• 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
• Tidal effects in the gravitational-wave phase evolution of compact binary systems to next-to-next-to-leading post-Newtonian order
• Comparing two models for measuring the neutron star equation of state from gravitational-wave signals
• Tidal effects in quantum field theory
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Hilbert Series for Flavor Invariants of the Standard Model
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios
• On higher-derivative effects on the gravitational potential and particle bending
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• Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order
• Constraining extra-spatial dimensions with observations of GW170817
• GW170817 constraints on the properties of a neutron star in the presence of WIMP dark matter
• Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity
• Can we probe Planckian corrections at the horizon scale with gravitational waves?
• Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order
• Post-Minkowskian Hamiltonians in Modified Theories of Gravity

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