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Resummed energy loss in extreme-mass-ratio scattering using critical orbits

Leor Barack1,*, Riccardo Gonzo2,†, Benjamin Leather1,‡, Oliver Long3,§, and Niels Warburton4,∥

  • *Contact author: L.Barack@soton.ac.uk
  • †Contact author: r.gonzo@qmul.ac.uk
  • ‡Contact author: B.J.Leather@soton.ac.uk
  • §Contact author: oliver.long@aei.mpg.de
  • ∥Contact author: niels.warburton@ucd.ie
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Phys. Rev. D 113, 104042 – Published 19 May, 2026

DOI: https://doi.org/10.1103/pxzz-dl2b

Abstract

Motivated by recent efforts to bridge between weak- and strong-field descriptions of black-hole binary dynamics, we develop a resummation scheme for post-Minkowskian radiative observables in extreme-mass-ratio scattering, augmented with post-Newtonian terms. Specifically, we derive universal interpolation formulas for the total energy emitted in gravitational waves out to infinity and down the event horizon of the large black hole, valid to leading order in the small mass ratio. We test our formulas using numerical results from direct calculations in black hole perturbation theory. The central idea of our approach is to utilize as a strong-field diagnostic the known form of divergence in the radiated energy along geodesics near the parameter-space separatrix between scattering and plunge. The dominant, logarithmic term of this divergence can be expressed in terms of instantaneous energy fluxes calculated along the unstable circular geodesics that form the separatrix, fluxes that we obtain using interpolation of highly accurate numerical data. The same idea could be applied to bound-orbit radiative observables via either unbound-to-bound mapping or a direct resummation of bound-orbit post-Newtonian expressions.

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Phys. Rev. D 113, 104042– Published 19 May, 2026
  • Received 12 February 2026
  • Accepted 17 April 2026
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