Dynamical quasinormal mode excitation II: propagation and convergence in Schwarzschild

TL;DR

This paper advances understanding of black hole quasinormal mode excitation during particle plunge, introducing a refined propagation prescription and revealing a transition in QNM behavior at the bounce radius.

Contribution

It provides a new, more accurate method for modeling QNM propagation and explains the transition from quasi-resonant to free-oscillator regimes during black hole plunge.

Findings

Confirmed existence of bounce radius at r*=0 affecting QNM scattering

Achieved accurate reproduction of waveform oscillations after bounce crossing

Identified transition in QNM behavior from destructive interference to rapid convergence

Abstract

We study the dynamical excitation of quasinormal modes (QNMs) during the plunge of a particle into a Schwarzschild black hole, building on the framework of Phys. Rev. D 113 (2026) 2, 024048 (Paper I). Investigating the high-frequency behavior of Leaver's QNM solutions, we obtain a more accurate and general prescription for their propagation. We confirm the existence of a new "characteristic radius" for QNM excitation, the bounce radius $r_*=0$, in agreement with recent literature. To its right, the QNM signal scatters off this point before reaching the observer; to its left, it propagates directly on the light-cone. Applying the formalism of Paper I to inspiralling particles, and using this refined prescription, we obtain a QNM signal that accurately reproduces the oscillatory component of the waveform after the bounce crossing, yielding an essentially complete first-principles description of the waveform from shortly after the signal peak. The dynamical QNM signal undergoes a transition as the particle crosses the bounce radius: from a quasi-resonant regime, where successive overtones are driven in counter-phase and interfere destructively, to a free-oscillator one, where they are in phase and the QNM sum converges rapidly. These results provide a clear physical interpretation of the collective QNM behavior during the plunge, and a firm theoretical foundation for accurate ringdown modelling.