Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory

Abstract

A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small velocities), and employs a new dictionary focussing on the functional dependence of the scattering angle on the total energy and the total angular momentum of the system. Using this approach, we prove to all orders in v/c two results that were previously known to hold only to a limited post-Newtonian accuracy: (i) the relativistic gravitational dynamics of a two-body system is equivalent, at first post-Minkowskian order, to the relativistic dynamics of an effective test particle moving in a Schwarzschild metric; and (ii) this equivalence requires the existence of an exactly quadratic map between the real (relativistic) two-body energy and the (relativistic) energy of the effective particle. The same energy map is also shown to apply to the effective one-body description of two masses interacting via tensor-scalar gravity.

12 pages, 1 figure

References in corpus (9)

• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• Fourth post-Newtonian effective one-body dynamics
• A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation

Cited by in corpus (23)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• A worldsheet for Kerr
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• Infrared features of gravitational scattering and radiation in the eikonal approach
• Classical observables from coherent-spin amplitudes
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Einstein, Planck and Vera Rubin: relevant encounters between the Cosmological and the Quantum Worlds
• From Boundary Data to Bound States III: Radiative Effects
• Kerr-Newman from Minimal Coupling
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Eikonal Scattering in Kaluza-Klein Gravity
• Computational Techniques for Parameter Estimation of Gravitational Wave Signals
• Analytic Approximations in GR and Gravitational Waves
• Probing Particle Physics with Gravitational Waves
• Classical gravitational scattering from a gauge-invariant double copy
• First Post-Minkowskian approach to turbulent gravity