Collective filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers

Ma, Sizheng; Mitman, Keefe; Sun, Lei; Deppe, Nils; Hébert, François; Kidder, Lawrence E.; Moxon, Jordan; Throwe, William; Fischer, Nils; Chen, Yanbei

doi:10.48550/arxiv.2207.10870

Cited by 3 publications

(4 citation statements)

References 164 publications

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“…Since the sensitivity of GW detectors will increase in the coming years [25][26][27][28], there is the potential to observe nonlinear ringdown effects in high signal-to-noise ratio (SNR) events. A few previous works have shown that second-order perturbation effects can be identified in some NR simulations of binary BH mergers [29,30]. In this Letter we show that quadratic QNMs-the damped sinusoids coming from second-order perturbation theory in GR-are a ubiquitous effect present in simulations across various binary mass ratios and remnant BH spins.…”

supporting

confidence: 50%

Nonlinearities in Black Hole Ringdowns

et al. 2023

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supporting

confidence: 50%

Nonlinearities in Black Hole Ringdowns

et al. 2023

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“…Therefore, future analyses must be careful when using linear QNMs frequencies to describe higher harmonics. Indeed, the recent study in [53] has also shown evidence of quadratic QNMs in ( = 5, |m| = 4) and ( = 5, |m| = 5) harmonics in at least one specific binary merger simulation. Furthermore, higher harmonics are expected to be important in future GW data.…”

Section: Introductionmentioning

confidence: 92%

Generation and propagation of nonlinear quasinormal modes of a Schwarzschild black hole

Lagos

Hui

2023

Phys. Rev. D

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In the analysis of a binary black hole coalescence, it is necessary to include gravitational self-interactions in order to describe the transition of the gravitational wave signal from the merger to the ringdown stage. In this paper we study the phenomenology of the generation and propagation of nonlinearities in the ringdown of a Schwarzschild black hole, using second-order perturbation theory. Following earlier work, we show that the Green's function and its causal structure determines how both first-order and second-order perturbations are generated, and hence highlight that both of these solutions share some physical properties. In particular, we discuss the sense in which both linear and quadratic quasi-normal modes (QNMs) are generated in the vicinity of the peak of the gravitational potential barrier (loosely referred to as the light ring). Among the second-order perturbations, there are solutions with linear QNM frequencies (whose amplitudes are thus renormalized from their linear values), as well as quadratic QNM frequencies with a distinct spectrum. Moreover, we show using a WKB analysis that, in the eikonal limit, waves generated inside the light ring propagate towards the black hole horizon, and only waves generated outside propagate towards an asymptotic observer. These results might be relevant for recent discussions on the validity of perturbation theory close to the merger. Finally, we argue that even if nonlinearities are small, quadratic QNMs may be detectable and would likely be useful for improving ringdown models of higher angular harmonics and future tests of gravity.

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“…1 On the one hand, this requires pushing black hole perturbation theory up to second order, a task which was undertaken by various authors in the last decades [11][12][13][14][15][16][17][18]. On the other hand, the non-linearities can be investigated numerically, a target which has attracted considerable attention recently [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] (see [36] for a recent prospect on the detectability of these non-linearities). While the spectrum of quadratic QNMs (dubbed QQNMs) has a straightforward relationship to the linear spectrum, the fate of the amplitude of quadratic perturbations has been addressed only recently [37,38].…”

Section: Introductionmentioning

confidence: 99%

“…While the spectrum of quadratic QNMs (dubbed QQNMs) has a straightforward relationship to the linear spectrum, the fate of the amplitude of quadratic perturbations has been addressed only recently [37,38]. Numerical investigations have shown that the amplitude of the quadratic modes depends on the multipole structure, dominating in some cases the one of their linear counterparts for large multipoles [19][20][21][22]. This growing body of results reveals that the black hole spectroscopy program is more delicate than anticipated and underlines the necessity to further investigate the response of black holes to perturbations beyond the linear regime.…”

Section: Introductionmentioning

confidence: 99%

Quadratic perturbations of the Schwarzschild black hole: the algebraically special sector

Achour,

Roussille

2024

J. Cosmol. Astropart. Phys.

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We investigate quadratic algebraically special perturbations (ASPs) of the Schwarzschild black hole. Their dynamics are derived from the expansion up to second order in perturbation of the most general algebraically special twisting vacuum solution of general relativity. Following this strategy, we present analytical expressions for the axial-axial, polar-polar and polar-axial source terms entering in the dynamical equations. We show that these complicated inhomogeneous equations can be solved analytically and we present explicit expressions for the profiles of the quadratic ASPs. As expected, they exhibit exponential growth both at the past and future horizons even in the non-linear regime. We further use this result to analyze the quadratic zero modes and their interpretation in terms of quadratic corrections to mass and spin of the Schwarzschild black hole. The present work provides a direct extension beyond the linear regime of the original work by Couch and Newman.

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Collective filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers

Cited by 3 publications

References 164 publications

Nonlinearities in Black Hole Ringdowns

Nonlinearities in Black Hole Ringdowns

Generation and propagation of nonlinear quasinormal modes of a Schwarzschild black hole

Quadratic perturbations of the Schwarzschild black hole: the algebraically special sector

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