"Waveforms" at the Horizon

TL;DR

This work analyzes the scattering of a light particle off a Schwarzschild black hole in the post-Minkowskian regime, computing the perturbation induced on the horizon (the horizon waveform) for gravitational, electromagnetic, and scalar fields via the Teukolsky formalism. By solving the inhomogeneous Teukolsky equation with a Green's function approach and using horizon/infinty waveforms, the authors derive explicit leading PM expressions for the energy and angular momentum absorbed by the horizon, and verify consistency with known EFT results for energy absorption while presenting a new PM result for angular momentum absorption. The approach leverages a systematic PM expansion of confluent Heun solutions and a careful treatment of source terms along hyperbolic geodesics, yielding closed-form absorption formulas for each spin sector and performing nonrelativistic checks against horizon-reaction calculations. The results strengthen the bridge between black hole perturbation theory and EFT methods, with potential extensions to Kerr black holes and higher-dimensional spacetimes, and implications for understanding horizon dynamics under scattering and horizon symmetries.

Abstract

We study perturbations induced by a light particle scattering off a Schwarzschild black hole. Exploiting recent results for the wave propagation in this geometry, we derive the fields that this process induces on the horizon to leading order in the post-Minkowskian (PM) regime, when the light probe is far from the black hole. We then use these results to calculate the fluxes of energy and angular momentum that enter the black hole. We consider the effects due to gravitational, electromagnetic and scalar radiation, finding agreement with recent computations of the absorbed energy, while the absorbed angular momentum provides a new PM result.