An Amplitudes Approach to Spinning Black Hole Scattering
Abstract
The detection of gravitational waves has opened a new era of precision studies of gravity, demanding advances in our understanding of compact binary dynamics. Scattering amplitudes provide a powerful framework for studying these systems using methods from high-energy physics. In this thesis, we study classical black hole scattering, systematically including spin---an important feature of real astrophysical systems---to describe Kerr black hole dynamics. We model Kerr black holes as massive point particles in finite-spin representations and compute their scattering dynamics perturbatively. We resolve an ambiguity mixing classical and quantum contributions using our spin interpolation method, obtaining a classical amplitude for Kerr black hole scattering through quartic order in spin at third post-Minkowskian order. From this amplitude, we extract the gauge-invariant radial action, enabling the computation of classical non-aligned-spin observables---such as the linear and angular impulses---using covariant Dirac brackets. The amplitude exhibits spin-shift symmetry, remaining invariant under a shift of the black hole spin by the momentum transfer. Motivated by this property, we study the conserved quantities governing the scattering process and show that the dynamics of a probe black hole remains integrable at asymptotic infinity through quartic order in probe spin. Finally, we show that the quartic-in-spin radial action for a probe black hole in a Kerr background, at any order in perturbation theory, is completely fixed by the aligned-spin dynamics, provided that it satisfies asymptotic integrability and spin-shift symmetry.
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BibTeX
@misc{akpinar2026amplitudes,
title = {{An Amplitudes Approach to Spinning Black Hole Scattering}},
author = {Dogan Akpinar},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02272},
eprint = {2611.02272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02272},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Amplitudes Approach to Spinning Black Hole Scattering
AU - Dogan Akpinar
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02272
UR - https://arxiv.org/abs/2611.02272
AB - The detection of gravitational waves has opened a new era of precision studies of gravity, demanding advances in our understanding of compact binary dynamics. Scattering amplitudes provide a powerful framework for studying these systems using methods from high-energy physics. In this thesis, we study classical black hole scattering, systematically including spin---an important feature of real astrophysical systems---to describe Kerr black hole dynamics. We model Kerr black holes as massive point particles in finite-spin representations and compute their scattering dynamics perturbatively. We resolve an ambiguity mixing classical and quantum contributions using our spin interpolation method, obtaining a classical amplitude for Kerr black hole scattering through quartic order in spin at third post-Minkowskian order. From this amplitude, we extract the gauge-invariant radial action, enabling the computation of classical non-aligned-spin observables---such as the linear and angular impulses---using covariant Dirac brackets. The amplitude exhibits spin-shift symmetry, remaining invariant under a shift of the black hole spin by the momentum transfer. Motivated by this property, we study the conserved quantities governing the scattering process and show that the dynamics of a probe black hole remains integrable at asymptotic infinity through quartic order in probe spin. Finally, we show that the quartic-in-spin radial action for a probe black hole in a Kerr background, at any order in perturbation theory, is completely fixed by the aligned-spin dynamics, provided that it satisfies asymptotic integrability and spin-shift symmetry.
ER -