Expansion parameter for amplitudes-based treatment of radial infall

Identify a suitable expansion parameter that enables a perturbative, tree-level application of scattering-amplitude methods to describe the gravitational-wave emission from a two-body system undergoing radial infall (head-on collision) along the falling process.

Background

The paper discusses applying the scattering-amplitudes framework to gravitational-wave physics and notes that, while amplitudes have been successfully used for scattering problems, the radial infall (head-on collision) case is challenging within this framework.

In particular, the authors state that it is not yet clear what small parameter should control a perturbative expansion for the amplitudes-based description of the falling process at tree level. They mention ongoing attempts and suggest that near-critical non-radial infall with small impact parameter might offer an alternative small parameter in related settings.

References

However, the specific problem of radial infall is not easily treated neither at the tree level from the amplitudes, since it is not fully clear yet how to identify a suitable expansion parameter along the falling process.

— Radial fall: the gravitational waveform up to the second-and-half Post-Newtonian order  (2604.01699 - Bini et al., 2 Apr 2026) in Concluding remarks