High precision black hole scattering
Abstract
In this thesis we compute the impulse of a classical black hole scattering encounter in the Post-Minkowskian (PM) expansion - a weak-field expansion in Newton's constant G - up to the fifth order. We describe the black holes as point particles within an effective field theory framework and couple them through gravity. The classical equations of motion are solved diagrammatically using the worldline quantum field theory (WQFT) formalism, in which the solution with causal boundary conditions is encoded in tree-level Feynman diagrams built from graviton and worldline fields. The Feynman integrals arising at each order are reduced by advanced IBP reduction techniques and evaluated with the method of differential equations. We find that, in the solution of these integrals, periods over Calabi--Yau manifolds - familiar from string theory - appear and contribute to the classical impulse at the fifth Post-Minkowskian order. The results of this work are the first analytic results for the scattering observables at fifth Post-Minkowskian order, together with the appearance of Calabi--Yau threefold periods in a classical physics observable.
Versions
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BibTeX
@misc{sauer2026high,
title = {{High precision black hole scattering}},
author = {Benjamin Sauer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31238},
eprint = {2610.31238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31238},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High precision black hole scattering
AU - Benjamin Sauer
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31238
UR - https://arxiv.org/abs/2610.31238
AB - In this thesis we compute the impulse of a classical black hole scattering encounter in the Post-Minkowskian (PM) expansion - a weak-field expansion in Newton's constant G - up to the fifth order. We describe the black holes as point particles within an effective field theory framework and couple them through gravity. The classical equations of motion are solved diagrammatically using the worldline quantum field theory (WQFT) formalism, in which the solution with causal boundary conditions is encoded in tree-level Feynman diagrams built from graviton and worldline fields. The Feynman integrals arising at each order are reduced by advanced IBP reduction techniques and evaluated with the method of differential equations. We find that, in the solution of these integrals, periods over Calabi--Yau manifolds - familiar from string theory - appear and contribute to the classical impulse at the fifth Post-Minkowskian order. The results of this work are the first analytic results for the scattering observables at fifth Post-Minkowskian order, together with the appearance of Calabi--Yau threefold periods in a classical physics observable.
ER -