Exact Cancellation of Horizon Modes in Kerr Ringdown

Abstract

Ringdown gravitational waves probe black hole spacetimes via quasinormal modes (QNMs). Recent studies have reported oscillatory features in QNM-filtered waveforms, and have led to conflicting interpretations as to whether they represent a near-horizon "direct wave". Reexamining a particle plunging into a Kerr black hole, we show that the saddle-point approximation underlying the proposed interpretation fails near the horizon. Our exact analysis reveals that every source-induced horizon-mode pole is canceled by an infinite tower of Matsubara zeros, independently of orbital and black-hole parameters. The first four stages of this sequential screening are also confirmed by time-domain numerical integration. Thus, within the near-horizon perturbative framework, source-induced horizon-mode signals do not survive at late times.