Ultrarelativistic scattering losses away from the separatrix

Analyze the ultrarelativistic limit of the energy and angular-momentum losses for Schwarzschild scattering orbits outside the separatrix limit, including the behavior of the generally nonuniform bounded-remainder terms as the light-ring limit is approached.

Background

The paper derives the leading divergent contributions to the energy and angular-momentum losses for scattering orbits as the incoming angular momentum approaches the capture threshold at fixed particle energy. These losses are controlled by the fluxes from the corresponding unstable circular orbit and, in the ultrarelativistic limit, inherit the light-ring divergence.

The authors explicitly caution that the O(1) remainder in the separatrix expansion is not necessarily uniformly bounded as the circular-orbit radius approaches the light ring. Consequently, the paper does not determine the complete ultrarelativistic behavior of scattering losses away from the separatrix limit.

References

We leave a full analysis of the ultrarelativistic limit of scattering losses outside the separatrix limit for future work.

— Towards ultrarelativistic scattering near the light ring: asymptotic divergence of gravitational-wave fluxes  (2610.20708 - Trestini et al., 14 Oct 2026) in Section 1, Introduction, paragraph following Eqs. (3a)–(3b)

A complete derivation of Eq.~eq:Flm_WKB_Kerr requires expanding the circular source and matching the local radial solutions to the boundary conditions at infinity and the horizon, which is left for future work.

— Towards ultrarelativistic scattering near the light ring: asymptotic divergence of gravitational-wave fluxes  (2610.20708 - Trestini et al., 14 Oct 2026) in Section 6, “Conjecture for Kerr fluxes,” final paragraph