Spinning black hole binary dynamics, scattering amplitudes, and effective field theory
Journal
Physical Review D
Journal Volume
104
Journal Issue
6
Start Page
065014
ISSN
2470-0010
2470-0029
Date Issued
2021-09-17
Author(s)
Abstract
We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably chosen effective field theory, we obtain the spin1-spin2 terms of a two-body effective Hamiltonian through O(G2) and valid to all orders in velocity. Solving Hamilton's equations yields the impulse and spin changes of the individual bodies. We write them in a surprisingly compact form as appropriate derivatives of the eikonal phase obtained from the amplitude. It seems likely this structure persists to higher orders. We also point out various double-copy relations for general spin.
Publisher
American Physical Society (APS)
Type
journal article