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Spinning self-force EFT: 1SF waveform recursion relation and Compton scattering

Dogan Akpinar1,*, Vittorio del Duca2,†, and Riccardo Gonzo1,‡

  • 1Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
  • 2INFN, Laboratori Nazionali di Frascati, 00044 Frascati (RM), Italy

  • *Contact author: dogan.akpinar@ed.ac.uk
  • †Contact author: Vittorio.DelDuca@lnf.infn.it
  • ‡Contact author: rgonzo@ed.ac.uk
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Phys. Rev. D 112, 084014 – Published 7 October, 2025

DOI: https://doi.org/10.1103/fs74-84v6

Abstract

Building on recent approaches, we develop an effective field theory for the interaction of spinning particles modeling Kerr black holes within the gravitational self-force expansion. To incorporate dimensional regularization into this framework, we analyze the higher-dimensional metric arising from the minimal coupling solution, comparing it against the Myers-Perry black hole and its particle description. We then derive the 1SF self-force effective action up to quadratic order in the spin expansion, identifying a new type of spinning recoil term that arises from integrating out the heavy dynamics. Next, we study the 1SF metric perturbation both from the traditional self-force perspective and through the diagrammatic background field expansion, making contact with the radiative waveform. This leads us to consider a novel recursion relation for the curved space 1SF Compton amplitude, which we study up to one-loop in the wave regime and compare with the flat space one-loop Compton for Kerr up to quadratic order in spin. Finally, we investigate the 1SF spinning Compton amplitude in the eikonal regime, clarifying how the strong-field effect—such as the location of the separatrix—emerges from the resummation of the perturbative weak-field expansion.

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Phys. Rev. D 112, 084014– Published 7 October, 2025
  • Received 18 April 2025
  • Accepted 7 August 2025
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