Alejandro Svyatkovskyy Kholyavka

arXiv2026

Spectral suppression of black hole ringdown tails

The late-time power law tail predicted by Price's law is a generic feature of black hole perturbation theory, yet it is largely absent in numerical relativity waveforms of binary black hole mergers. We show that this suppression arises from the spectral structure of oscillatory sources. For a generic perturbation with carrier frequency $ν$ and characteristic width $σ$, the branch-cut excitation coefficient governing the tail is suppressed by $α=σν$. For a Gaussian pulse, the suppression $\sim e^{-α^2/2}$. This suppression is exact and confirmed by the time domain Regge Wheeler evolutions. The same parameter that controls the transition from broadband to frequency selective black hole response is also responsible for the tail suppression. Moreover, we analytically derive the leading- and next-to-leading-order tail coefficients, finding agreement with numerical fits below the $\sim10\%$ level. Our results provide a first principle explanation for the absence of tails in quasi-circular mergers and their enhancement in head-on and eccentric ones.

gr-qc↗

arXiv2026

Shaping black hole resonances I. Black hole ringdown as a spectral filtering process

The ringdown of a perturbed black hole (BH) can be described as a superposition of quasinormal modes (QNMs), whose frequencies are determined by the spacetime geometry while their amplitudes depend also on the perturbing source. However, the physical mechanism governing mode excitation remains unclear and is typically treated on a case by case basis. In this work, we show that QNM excitation is governed by a simple spectral rule: each mode is excited according to the Fourier content of the perturbation evaluated at its characteristic frequency. This result follows from the factorization of the excitation coefficients and establishes a direct, quantitative connection between the spectral properties of the perturbation and the resulting ringdown amplitudes. To make this mechanism explicit and controllable, we construct localized perturbations with independently tunable spectral bandwidth and carrier frequency. We demonstrate analytically and numerically that BHs act as resonant spectral filters. We show analytically that the excitation amplitude of each mode equals the weighted spatial Fourier transform of the initial data evaluated at wavenumber $k\simω_n$ so that the filter selectively excites modes whose frequencies lie within the spectral support of the perturbation while suppressing others. Consequently, the excitation is maximized when the dominant perturbation frequency lies close to the real part of the QNM frequency, and we validate this at the percent level with fits to time-domain numerical evolutions. To robustly perform these fits, we have developed a new fitting algorithm, $\mathtt{QNMToolkit}$, which performs ringdown fits over large ensembles of sliding time-domain windows and quantifies the resulting fitting variance.

gr-qc↗