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Radiated angular momentum from spinning black hole scattering trajectories

Gustav Mogull1,2,3,*, Jan Plefka1,†, and Kathrin Stoldt1,‡

  • *Contact author: g.mogull@qmul.ac.uk
  • †Contact author: jan.plefka@hu-berlin.de
  • ‡Contact author: kathrin.stoldt.1@hu-berlin.de
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Phys. Rev. D 112, 124076 – Published 26 December, 2025

DOI: https://doi.org/10.1103/my38-14k5

Abstract

Using the worldline quantum field theory approach, we derive solutions to the equations of motion for spinning massive bodies up to quadratic order in spins. At leading post-Minkowskian (PM) order, these trajectories are obtained in the time domain, and at subleading order, they are obtained in the frequency domain. Our approach incorporates diagrammatic techniques and modern Feynman integration technologies and includes a family of loop integrals different to those seen in asymptotic PM calculations. Our results provide a new mechanism for computing the radiated angular momentum involved in gravitational scattering, which we reproduce at 2PM order up to linear spins. We have established a framework for computing higher-order effects to further extend the high-precision frontier in analytical gravitational wave physics and push predictions for the radiated angular momentum to higher perturbative orders.

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Phys. Rev. D 112, 124076– Published 26 December, 2025
  • Received 10 July 2025
  • Accepted 1 December 2025
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