A Caltech Library Service

Radiative Classical Gravitational Observables at O(G³) from Scattering Amplitudes

Herrmann, Enrico and Parra-Martinez, Julio and Ruf, Michael S. and Zeng, Mao (2021) Radiative Classical Gravitational Observables at O(G³) from Scattering Amplitudes. . (Unpublished)

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N=8 supergravity in the formalism of Kosower, Maybee, and O'Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at O(G³) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Herrmann, Enrico0000-0002-3983-2993
Parra-Martinez, Julio0000-0003-0178-1569
Ruf, Michael S.0000-0001-6770-2822
Zeng, Mao0000-0002-4741-4038
Alternate Title:Radiative Classical Gravitational Observables at O(G3) from Scattering Amplitudes
Additional Information:We are specially grateful to Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, and Gabriele Veneziano for stimulating discussions and for sharing a draft of their work [103] with us and for comments on our manuscript. We also thank Zvi Bern, Radu Roiban, Chia-Hsien Shen, and Mikhail Solon for helpful comments and collaboration on related projects; and Clifford Cheung and Rafael Porto for discussions. E.H. thanks Lance Dixon and Bernhard Mistlberger for discussions about the reverse unitarity method. E.H. is supported by the U.S. Department of Energy (DOE) under Award Number DE-SC0009937. J.P.-M. is supported by the U.S. Department of Energy (DOE) under Award Number DESC0011632. M.S.R.’s work is funded by the German Research Foundation (DFG) within the Research Training Group GRK 2044. M.Z.’s work is funded by the U.K. Royal Society through Grant URF\R1\20109.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009937
Department of Energy (DOE)DE-SC0011632
Deutsche Forschungsgemeinschaft (DFG)GRK 2044
Royal SocietyURF\R1\20109
Record Number:CaltechAUTHORS:20210412-100004574
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108692
Deposited By: Tony Diaz
Deposited On:12 Apr 2021 17:15
Last Modified:12 Apr 2021 17:15

Repository Staff Only: item control page