Waveform stability of black hole ringdown with stochastic horizon structure
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学科学学院）
We examine the robustness of black hole ringdown to stochastic horizon-scale structure within an effective field framework in a proof-of-principle Schwarzschild setup.Consistent with the understanding that the spectral instability of quasinormal modes does not necessarily imply observational breakdown, our results demonstrate that the macroscopic gravitational waveform remains robust. We identify the phase averaging mechanism as the physical origin of this stability, demonstrating that the spatial integration of the wave equation efficiently attenuates ultraviolet geometric details below the resolution limit of the probing wavelength. Building on the scaling law $\mathcal{M} \propto ε^2$ and the characteristic mismatch profile with respect to $L_c$, we propose a geometric selection rule for observability: a detectable signal imposes a strict dual constraint requiring both macroscopic spatial coherence ($L_c \sim M$) and classical-level intensity ($ε\gtrsim 10^{-4}$). This criterion quantitatively rules out the observability of incoherent, high-entropy quantum foam in the present static Schwarzschild model, suggesting that any significant ringdown deviation would instead serve as evidence for macroscopically coherent horizon structures.
We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our procedure relies on a {\it multiplicative} decomposition of $h(t)$ as the product of the fundamental quasi-normal mode with a remaining time-dependent complex factor whose amplitude and phase are separately fitted. As an illustrative example, we apply our analysis and fitting procedure to the ringdown part o…
We present an analytical waveform family describing gravitational waves (GWs) from the inspiral, merger and ringdown of non-spinning black-hole binaries including the effect of several non-quadrupole modes [($\ell = 2, m = \pm 1), (\ell = 3, m = \pm 3), (\ell = 4, m = \pm 4)$ apart from $(\ell = 2, m=\pm2)$]. We first construct spin-weighted spherical harmonics modes of hybrid waveforms by matching numerical-relativity simulations (with mass ratio $1-10$) describing the late inspiral, merger and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspir…
The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass non-spinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of ~0.1 radian when measured from the beginning of the simulation, and ~0.02 radian when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to ~0.01 radian in phase. The phase difference between t…
We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.
We describe a general procedure to generate spinning, precessing waveforms that include inspiral, merger and ringdown stages in the effective-one-body (EOB) approach. The procedure uses a precessing frame in which precession-induced amplitude and phase modulations are minimized, and an inertial frame, aligned with the spin of the final black hole, in which we carry out the matching of the inspiral-plunge to merger-ringdown waveforms. As a first application, we build spinning, precessing EOB waveforms for the gravitational modes l=2 such that in the nonprecessing limit those waveforms agree wit…
This paper presents an algorithm to accelerate the evaluation of inspiral-merger-ringdown waveform models for gravitational wave data analysis. While the idea can also be applied in the time domain, here we focus on the frequency domain, which is most typically used to reduced computational cost in gravitational wave data analysis. Our work extends the idea of multibanding, which has been developed to accelerate frequency domain waveforms, to include the merger and ringdown and spherical harmonics beyond the dominant quadrupole spherical harmonic. The original method is based on a heuristic al…
The waveforms from binary black hole mergers include inspiral, merger, and ringdown parts. Usually, the inspiral waveform can be obtained by calibrating from post-Newtonian approximation; The merger and ringdown ones can be gotten from the quasinormal modes with black hole perturbation theory. However, for more general black holes, the calculation of the quasinormal modes is not trivial. In this paper we use the photon sphere to get the quasinormal modes of spinning black holes. Then we connect the ringdown wave with the inspiral part to get full waveforms and compare with the ones from numeri…
Gravitational radiation from a slightly distorted black hole with ringdown waveform is well understood in general relativity. It provides a probe for direct observation of black holes and determination of their physical parameters, masses and angular momenta (Kerr parameters). For ringdown searches using data of gravitational wave detectors, matched filtering technique is useful. In this paper, we describe studies on problems in matched filtering analysis in realistic gravitational wave searches using observational data. Above all, we focus on template constructions, matches or signal-to-noise…
We numerically solve the Teukolsky equation in the time domain to obtain the gravitational-wave emission of a small mass inspiraling and plunging into the equatorial plane of a Kerr black hole. We account for the dissipation of orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes for circular, equatorial orbits, down to the light-ring. We consider Kerr spins $-0.99 \leq q \leq 0.99$, and compute the inspiral-merger-ringdown (2,2), (2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the large-spin regime, and find a great simplicity in the merger waveforms, thanks to …
Dissection of a merger-ringdown waveform in the small-mass-ratio limit
Radboud University（拉德堡德大学）；University of Southampton（南安普顿大学）；Universität Leipzig（莱比锡大学）；Scoil na Matamaitice agus na Staitisticí, An Coláiste Ollscoile, Baile Átha Cliath（都柏林三一学院数学与统计学院）；Centro Brasileiro de Pesquisas Físicas (CBPF)（巴西物理研究中心）
The post-merger signal in binary black hole merger is described by linear, black-hole perturbation theory. Historically, this has been modeled using the dominant positive-frequency (corotating) fundamental mode. Recently, there has been a renewed effort in modeling the post-merger waveform using higher, positive-frequency overtones in an attempt to achieve greater accuracy in describing the waveform at earlier times using linear perturbation theory. It has been shown that the inclusion of higher overtones can shift the linear regime to the peak of $(l,m)=(2,2)$ spherical harmonic mode. In this…
We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of non-spinning eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasi-circular NR waveforms. The use of circular merger waveforms is possible because eccentric binaries circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q = m_1/m_2 = 3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting ~20…
Systematic bias in LISA ringdown analysis due to waveform inaccuracy
SISSA（国际高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高级理工学院物理与天体物理中心）
We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime,…
According to General Relativity a perturbed black hole will return to a stable configuration by the emission of gravitational radiation in a superposition of quasi-normal modes. Such a perturbation will occur due to the coalescence of a black hole binary, following their inspiral and subsequent merger. At late times the waveform, which we refer to as a ringdown, is expected to be dominated by a single mode. As the waveform is well-known the method of matched filtering can be implemented to search for this signal using LIGO data. LIGO is sensitive to the dominant mode of perturbed black holes w…
We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass r…
The waveform templates of the matched filtering-based gravitational-wave search ought to cover wide range of parameters for the prosperous detection. Numerical relativity (NR) has been widely accepted as the most accurate method for modeling the waveforms. Still, it is well-known that NR typically requires a tremendous amount of computational costs. In this paper, we demonstrate a proof-of-concept of a novel deterministic deep learning (DL) architecture that can generate gravitational waveforms from the merger and ringdown phases of the non-spinning binary black hole coalescence. Our model tak…
Of all the astronomical sources of gravitational radiation, the ringdown waveform arising from a small perturbation of a spinning black hole is perhaps the best understood: for the late stages of such a perturbation, the waveform is simply an exponentially-damped sinusoid. Searching interferometric gravitational wave antenna data for these should be relatively easy. In this paper, I present the results of a single-filter search for ringdown waveforms arising from a 50 solar mass black hole with 98% of its maximum spin angular momentum using data from the Caltech 40-meter prototype interferomet…
Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multi-mode template of merger waveforms is the apparently complicated behavior of some of these modes; instea…
Gravitational-wave signals from black-hole binaries with non-precessing spins are described by four parameters -- each black hole's mass and spin. It has been shown that the dominant spin effects can be modeled by a \emph{single} spin parameter, leading to the development of several \emph{three-parameter} waveform models. Previous studies indicate that these models should be adequate for gravitational-wave detection. In this paper we focus on the systematic biases that would result from using them to estimate binary parameters, and consider a one-parameter family of configurations at one choic…
It is assumed that a black hole can be disturbed in such a way that a ringdown gravitational wave would be generated. This ringdown waveform is well understood and is modelled as an exponentially damped sinusoid. In this work we use this kind of waveform to study the performance of the SCHENBERG gravitational wave detector. This first realistic simulation will help us to develop strategies for the signal analysis of this Brazilian detector. We calculated the signal-to-noise ratio as a function of frequency for the simulated signals and obtained results that show that SCHENBERG is expected to b…
Electromagnetic radiation emitted by a charged particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole is examined. Both even- and odd-parity electromagnetic perturbations are considered. They are described by using gauge invariant master functions and the regularized multipolar waveforms as well as their unregularized counterparts constructed from the quasinormal-mode spectrum are obtained for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle. They are in excellent agreement and the resu…
It is known that approximating the Regge-Wheeler Potential with step functions significantly modifies the Schwarzschild black hole quasinormal mode spectrum. Surprisingly, this change in the spectrum has little impact on the ringdown waveform. We examine whether this issue is caused by the jump discontinuities and/or the piecewise constant nature of step functions. We show that replacing the step functions with a continuous piecewise linear function does not qualitatively change the results. However, in contrast to previously published results, we discover that the ringdown waveform can be app…
Avoided crossings and resonances in black hole ringdown with coupled fields: A case study of the Einstein-Maxwell-axion system
Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学理学研究系早期宇宙研究中心）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理学系）
Information about the neutron-star equation of state is encoded in the waveform of a black hole-neutron star system through tidal interactions and the possible tidal disruption of the neutron star. During the inspiral this information depends on the tidal deformability Lambda of the neutron star, and we find that Lambda is the best measured parameter during the merger and ringdown as well. We performed 134 simulations where we systematically varied the equation of state as well as the mass ratio, neutron star mass, and aligned spin of the black hole. Using these simulations we have developed a…
Ringdown Signatures of Dehnen Dark Matter Halos: Fluid Modes and Detectability with Space-Based Detectors
Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力国家实验室引力波实验中心）
We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2,2) mode and of the subleading modes (2,1), (3,3), (4,4) and (5,5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2,2) mode between model and numerical simulation remains below 0.1 rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2,2) mode is 2% and grows to 12% during the ringdow…
Using recent results from numerical relativity simulations of non-spinning binary black hole mergers we revisit the problem of detecting ringdown waveforms and of estimating the source parameters, considering both LISA and Earth-based interferometers. We find that Advanced LIGO and EGO could detect intermediate-mass black holes of mass up to about 1000 solar masses out to a luminosity distance of a few Gpc. For typical multipolar energy distributions, we show that the single-mode ringdown templates presently used for ringdown searches in the LIGO data stream can produce a significant event los…
Modeling the merger-ringdown of an eccentric test-mass inspiral into a Kerr black hole using the effective-one-body framework
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Maryland（马里兰大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）；University of Rhode Island（罗德岛大学）；University of Massachusetts, Dartmouth（马萨诸塞大学达特茅斯分校）
It is now possible to theoretically calculate the gravitational-wave signal from the inspiral, merger and ringdown of a black-hole-binary system. The late inspiral, merger and ringdown can be calculated in full general relativity using numerical methods. The numerical waveforms can then be either stitched to inspiral waveforms predicted by approximation techniques (in particular post-Newtonian calculations) that start at an arbitrarily low frequency, or used to calibrate free parameters in analytic models of the full waveforms. In this review I summarize the status of numerical-relativity (NR)…
Ringdown mode amplitudes of charged binary black holes
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学天体物理与天文卡弗里研究所）；Eberhard Karls University of Tübingen（蒂宾根大学）；Universitat de València（瓦伦西亚大学）；University of Arizona（亚利桑那大学）；AWS Center for Quantum Computing（亚马逊网络服务量子计算中心）；Sofia University “St. Kliment Ohridski”（索非亚大学）；Institute of Mathematics and Informatics, Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
We study the gravitational radiation emitted by a massive point particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. We consider both even- and odd-parity perturbations and describe them using the two gauge-invariant master functions of Cunningham, Price, and Moncrief. We obtain, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over of a large number of modes, and their unregularized counterparts co…
According to general relativity a perturbed black hole will settle to a stationary configuration by the emission of gravitational radiation. Such a perturbation will occur, for example, in the coalescence of a black hole binary, following their inspiral and subsequent merger. At late times the waveform is a superposition of quasi-normal modes, which we refer to as the ringdown. The dominant mode is expected to be the fundamental mode, l=m=2. Since this is a well-known waveform, matched filtering can be implemented to search for this signal using LIGO data. We present a search for gravitational…
In general relativity, the remnant object originating from an uncharged black hole merger is a Kerr black hole. The approach to this final state is reached through the emission of a late train of radiation known as the black hole ringdown. The ringdown morphology is described by a countably infinite set of damped sinusoids, whose complex frequencies are solely determined by the final black hole's mass and spin. Recent results advocate that ringdown waveforms from numerical relativity can be fully described from the peak of the strain onwards if quasi-normal mode models with $N_{max}=7$ overton…
For the first time, we construct an inspiral-merger-ringdown waveform model within the effective-one-body formalism for spinning, nonprecessing binary black holes that includes gravitational modes beyond the dominant $(\ell,|m|) = (2,2)$ mode, specifically $(\ell,|m|)=(2,1),(3,3),(4,4),(5,5)$. Our multipolar waveform model incorporates recent (resummed) post-Newtonian results for the inspiral and information from 157 numerical-relativity simulations, and 13 waveforms from black-hole perturbation theory for the (plunge-)merger and ringdown. We quantify the improved accuracy including higher-ord…
Modeling Direct Waves in Binary Black Hole Ringdowns
Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）；Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心应用数学与理论物理系）；Kavli Institute for Cosmology, University of Cambridge（剑桥大学卡弗里宇宙学研究所）
Identifying Exceptional Points in Black Hole Ringdowns
Nankai University（南开大学）；Yantai University（烟台大学）；The Hong Kong University of Science and Technology（香港科技大学）；The HKUST Jockey Club Institute for Advanced Study（香港科技大学赛马会高等研究院）
We discuss a new ringdown frequency mode for vacuum perturbations of the Kerr black hole. We evolve initial data for the vacuum radial Teukolsky equation using a near horizon approximation, and find a frequency mode analogous to that found in a recent study of radiation generated by a plunging particle close to the Kerr horizon. We discuss our results in the context of that study. We also explore the utility of this mode by fitting a numerical waveform with a combination of the usual quasi-normal modes (QNMs) and the new oscillation frequency.
