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  • Letter
  • Open Access

Unexpected symmetries of Kerr black hole scattering

Dogan Akpinar1,*, Graham R. Brown1,†, Riccardo Gonzo2,‡, and Mao Zeng1,§

  • 1Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
  • 2Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom

  • *Contact author: dogan.akpinar@ed.ac.uk
  • †Contact author: graham.brown@ed.ac.uk
  • ‡Contact author: r.gonzo@qmul.ac.uk
  • §Contact author: mao.zeng@ed.ac.uk
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Phys. Rev. D 113, L101501 – Published 5 May, 2026

DOI: https://doi.org/10.1103/dd5t-8dn5

Abstract

Motivated by the recent introduction of the Dirac bracket framework to compute spinning observables for the scattering of Kerr black holes, we initiate the study of conserved quantities from an on shell amplitude perspective. We establish new results for the conservation of energy, angular momentum, the Rüdiger invariant, and the quadrupolar Carter constant using the spinning radial action extracted from the literature both in the probe limit and beyond, up to third post-Minkowskian order in the conservative sector. Furthermore, we offer a new perspective on the spin-shift symmetry of the radial action, clarifying its role in the dynamics. Finally, we define a new on shell notion of asymptotic integrability in the Liouville sense and present strong evidence that it is surprisingly satisfied by a spinning probe in Kerr up to quartic order in the probe spin, to all orders in the post-Minkowskian expansion. We further establish integrability beyond the probe limit at low post-Minkowskian orders. Our results suggest important new implications for the dynamics of Kerr black holes.

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Phys. Rev. D 113, L101501– Published 5 May, 2026
  • Received 22 August 2025
  • Accepted 12 February 2026
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