The radial action from probe amplitudes to all orders

Uri Kol, Donal O’Connell, Ofri Telem*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT gravitational backgrounds. A characteristic relativistic effect, that scattering trajectories may wind around these sources any number of times, can be recovered when all-order amplitudes are available. We show that the amplitude for scattering a probe off a pure NUT is given by the solution of a transcendental equation involving continued fractions, and explain how to solve this equation to any desired loop order.

Original languageAmerican English
Article number141
JournalJournal of High Energy Physics
Issue number3
StatePublished - Mar 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).


  • Black Holes
  • Classical Theories of Gravity
  • Scattering Amplitudes
  • Spacetime Singularities


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