Prompt Response from Plunging Sources in Schwarzschild Spacetime

TL;DR

This paper provides a systematic analysis of the prompt response in gravitational waves from sources plunging into Schwarzschild black holes, enhancing understanding of waveform components during inspiral and merger.

Contribution

It offers a rigorous theoretical framework for the prompt response, quantifies its strength relative to quasinormal modes, and improves waveform reconstruction accuracy.

Findings

Prompt response is ~1.2 times stronger than quasinormal mode excitation during inspiral.

Prompt response decays rapidly near waveform peak, transitioning to ringdown.

Full waveform reconstruction achieves 99% accuracy by combining all components.

Abstract

Gravitational waves generated by moving sources in Schwarzschild spacetime can be decomposed into three principal components: quasinormal modes, tail, and prompt response. While the first two have been extensively studied, a systematic and exact treatment of the prompt response has received comparatively little attention. In this work, building on recent progress in elucidating the structure of the Green's function of the Regge-Wheeler equation, we place the prompt response on a firm theoretical footing and investigate its morphology for sources inspiraling and plunging into a Schwarzschild black hole. We find that during the inspiral phase, the prompt response is stronger than the dynamical excitation of quasinormal modes by a factor of ~1.2, with both contributions modulated by the instantaneous orbital motion. Near the waveform peak, the prompt response rapidly decays, while the quasinormal modes transition into the ringdown regime. By combining the prompt response, quasinormal modes, and tail contributions, we achieve an accurate reconstruction of the full time-domain inspiral-merger-ringdown waveform at the 99$\%$ level, thereby providing strong support for the accuracy of this decomposition. These results offer new insight into the transition from inspiral to merger and ringdown.