Mechanical angular momentum loss at 𝒪(G4) from static and radiative gravitons
Abstract
We determine the loss of mechanical angular momentum Lμloss of two gravitationally scattering bodies at 𝒪(G4) using worldline quantum field theory (WQFT). The gravitational memory effect, a phenomenon of the early- and late-time behaviour of the gravitational field, leads to static contributions to Lμloss. We illuminate how these arise: the linear memory contributes through so-called static correlators, while the nonlinear memory vanishes at this order due to symmetry considerations. The computation of the remaining, dynamical part resembles that of the 𝒪(G4) impulse. We generate its integrand using a reformulation of the WQFT Feynman rules that conserves four-momentum at every vertex and plainly exhibits the classical loops. The three-loop integrals are reduced to master integrals, whose differential equations and boundary matching in the post-Newtonian limit we describe in some detail. In contrast to conservative effects at this order, only polylogarithms appear. While individual contributions to the dynamical part are divergent, these cancel in Lμloss. The quadratic-in-radiation part of our result reproduces earlier results, while the complete result agrees with existing post-Newtonian results.
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BibTeX
@misc{bohnenblust2026mechanical,
title = {{Mechanical angular momentum loss at $\mathcalO(G^4)$ from static and radiative gravitons}},
author = {Lara Bohnenblust and Carl Jordan Eriksen and Gustav Uhre Jakobsen and Kathrin Stoldt and Andrii Yanovets},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26822},
eprint = {2610.26822},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26822},
}
RIS
TY - UNPB
TI - Mechanical angular momentum loss at 𝒪(G^4) from static and radiative gravitons
AU - Lara Bohnenblust
AU - Carl Jordan Eriksen
AU - Gustav Uhre Jakobsen
AU - Kathrin Stoldt
AU - Andrii Yanovets
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26822
UR - https://arxiv.org/abs/2610.26822
AB - We determine the loss of mechanical angular momentum L^μ_loss of two gravitationally scattering bodies at 𝒪(G^4) using worldline quantum field theory (WQFT). The gravitational memory effect, a phenomenon of the early- and late-time behaviour of the gravitational field, leads to static contributions to L^μ_loss. We illuminate how these arise: the linear memory contributes through so-called static correlators, while the nonlinear memory vanishes at this order due to symmetry considerations. The computation of the remaining, dynamical part resembles that of the 𝒪(G^4) impulse. We generate its integrand using a reformulation of the WQFT Feynman rules that conserves four-momentum at every vertex and plainly exhibits the classical loops. The three-loop integrals are reduced to master integrals, whose differential equations and boundary matching in the post-Newtonian limit we describe in some detail. In contrast to conservative effects at this order, only polylogarithms appear. While individual contributions to the dynamical part are divergent, these cancel in L^μ_loss. The quadratic-in-radiation part of our result reproduces earlier results, while the complete result agrees with existing post-Newtonian results.
ER -