Modeling QNMs-Filtered Gravitational Waveforms: Approximation Limits and Filtering Effects
Abstract
The waveform left after quasinormal modes filtering of binary gravitational waveforms, often called the direct wave, has recently attracted considerable debate. Analytic models of this residual waveform involve several levels of approximation, while the effects of filtering on the modeling remain unclear. These issues require further investigation. In this paper, we examine the approximation errors, limits of applicability, and role of filtering in these models. We find that the point-particle models examined here show notable discrepancies with the filtered Binary-black-hole waveforms. Analytic particle templates based on the stationary-phase approximation perform reasonably well for the (ℓ,m)=(2,2) multipole, but exhibit substantial limitations for the (4,4). Although the filter is all-pass, it substantially affects the modeling results. Our analytic calculations on a Schwarzschild background further show that vacuum perturbations with Gaussian initial data can also exhibit direct-wave-like waveforms after filtering, with their morphology depending on the location of the initial data relative to the light ring.
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BibTeX
@misc{shi2026modeling,
title = {{Modeling QNMs-Filtered Gravitational Waveforms: Approximation Limits and Filtering Effects}},
author = {Jun-Xi Shi and Zhen-Tao He and Tingyuan Jiang and Yu Tian and Dan-Dan Yuan and Hongbao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30031},
eprint = {2610.30031},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30031},
}
RIS
TY - UNPB
TI - Modeling QNMs-Filtered Gravitational Waveforms: Approximation Limits and Filtering Effects
AU - Jun-Xi Shi
AU - Zhen-Tao He
AU - Tingyuan Jiang
AU - Yu Tian
AU - Dan-Dan Yuan
AU - Hongbao Zhang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30031
UR - https://arxiv.org/abs/2610.30031
AB - The waveform left after quasinormal modes filtering of binary gravitational waveforms, often called the direct wave, has recently attracted considerable debate. Analytic models of this residual waveform involve several levels of approximation, while the effects of filtering on the modeling remain unclear. These issues require further investigation. In this paper, we examine the approximation errors, limits of applicability, and role of filtering in these models. We find that the point-particle models examined here show notable discrepancies with the filtered Binary-black-hole waveforms. Analytic particle templates based on the stationary-phase approximation perform reasonably well for the (ℓ,m)=(2,2) multipole, but exhibit substantial limitations for the (4,4). Although the filter is all-pass, it substantially affects the modeling results. Our analytic calculations on a Schwarzschild background further show that vacuum perturbations with Gaussian initial data can also exhibit direct-wave-like waveforms after filtering, with their morphology depending on the location of the initial data relative to the light ring.
ER -