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Published April 30, 2021 | Submitted + Supplemental Material + Published
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Scattering Amplitudes and Conservative Binary Dynamics at O(G⁴)


Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G⁴). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G³) via its relation to the tail effect.

Additional Information

© 2021 Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3. Received 4 February 2021; accepted 11 March 2021; published 26 April 2021. We thank Samuel Abreu, Johannes Blümlein, Alessandra Buonanno, Clifford Cheung, Thibault Damour, Lance Dixon, Enrico Herrmann, Andrés Luna, Rafael Porto, Ira Rothstein, Jan Steinhoff, Gabriele Veneziano, and Justin Vines for helpful discussions. Z. B. is supported by the U.S. Department of Energy (DOE) under Award No. DE-SC0009937. J. P.-M. is supported by the U.S. Department of Energy (DOE) under Award No. DE-SC0011632. R. R. is supported by the U.S. Department of Energy (DOE) under Grant No. DE-SC0013699. M. S. R.'s work is funded by the German Research Foundation (DFG) within the Research Training Group GRK 2044. C.-H. S. is supported by the U.S. Department of Energy (DOE) under Award No. DE-SC0009919. M. P. S. is supported by the David Saxon Presidential Term Chair. M. Z.'s work is supported by the U.K. Royal Society through Grant No. URF\R1\20109. We thank the Mani L. Bhaumik Institute for support.

Attached Files

Published - PhysRevLett.126.171601.pdf

Submitted - 2101.07254.pdf

Supplemental Material - Hamiltonian_4PM.m


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August 20, 2023
October 23, 2023