Spinning black hole binary dynamics, scattering amplitudes, and effective field theory

Zvi Bern, Andres Luna, Radu Roiban, Chia Hsien Shen, Mao Zeng

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101 Scopus citations


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.

Original languageEnglish (US)
Article number065014
JournalPhysical Review D
Issue number6
StatePublished - Sep 15 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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