We derive an analytical expression for extracting the gravitational waveforms at null infinity using the Weyl scalar $ψ_4$ measured at a finite radius. Our expression is based on a series solution in orders of 1/r to the equations for gravitational perturbations about a spinning black hole. We compute this expression to order $1/r^2$ and include the spin parameter $a$ of the Kerr background. We test the accuracy of this extraction procedure by measuring the waveform for a merging black-hole binary at ten different extraction radii (in the range r/M=75-190) and for three different resolutions in the convergence regime. We find that the extraction formula provides a set of values for the radiated energy and momenta that at finite extraction radii converges towards the expected values with increasing resolution, which is not the case for the `raw' waveform at finite radius. We also examine the phase and amplitude errors in the waveform as a function of observer location and again observe the benefits of using our extraction formula. The leading corrections to the phase are ${\cal O}(1/r)$ and to the amplitude are ${\cal O}(1/r^2)$. This method provides a simple and practical way of estimating the waveform at infinity, and may be especially useful for scenarios such as well separated binaries, where the radiation zone is far from the sources, that would otherwise require extended simulation grids in order to extrapolate the `raw' waveform to infinity. Thus this method saves important computational resources and provides an estimate of errors.
The parameterized post-Einsteinian framework modifies inspiral waveform models to incorporate effects beyond General Relativity. We extend the existing model into the merger-ringdown regime. The modification introduced here adds a single degree of freedom that corresponds to a change in the binary coalescence time. Other merger properties remain as predicted by GR. We discuss parameter estimation with this model, and how it can be used to extract information from beyond-GR waveforms.
Extending our previous studies, we perform high-resolution simulations of inspiraling binary neutron stars in numerical relativity. We thoroughly carry through a convergence study in our currently available computational resources with the smallest grid spacing of $\approx 63$--86~meter for the neutron-star radius 10.9--13.7\,km. The estimated total error in the gravitational-wave phase is of order 0.1~rad for the total phase of $\gtrsim 210$\,rad in the last $\sim 15$--16 inspiral orbits. We then compare the waveforms (without resolution extrapolation) with those calculated by the latest effe…
We compare and contrast the emission of gravitational waves and waveforms for the recently established "helicoidal-drifting-sequence" of a test particle around a Kerr black hole with the publicly available waveform templates of numerical-relativity. The merger of two black holes of comparable mass are considered. We outline a final smooth merging of the test particle into the final Kerr black hole. We find a surprising and unexpected agreement between the two treatments if we adopt, for the mass of the particle and the Kerr black hole a Newtonian-center-of-mass description, and for the Kerr bl…
The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in $(3+1)$-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We …
Gravitational-wave observations of binary black holes allow new tests of general relativity to be performed on strong, dynamical gravitational fields. These tests require accurate waveform models of the gravitational-wave signal, otherwise waveform errors can erroneously suggest evidence for new physics. Existing waveforms are generally thought to be accurate enough for current observations, and each of the events observed to date appears to be individually consistent with general relativity. In the near future, with larger gravitational-wave catalogs, it will be possible to perform more strin…
We apply common gravitational wave inference procedures on binary black hole merger waveforms beyond general relativity. We consider dynamical Chern-Simons gravity, a modified theory of gravity with origins in string theory and loop quantum gravity. This theory introduces an additional parameter $\ell$, corresponding to the length-scale below which beyond-general-relativity effects become important. We simulate data based on numerical relativity waveforms produced under an approximation to this theory, which differ from those of general relativity in the strongly nonlinear merger regime. We co…
We reanalyze gravitational waves from binary-neutron-star mergers GW170817 and GW190425 using a numerical-relativity (NR) calibrated waveform model, the TF2+_Kyoto model, which includes nonlinear tidal terms. For GW170817, by imposing a uniform prior on the binary tidal deformability $\tildeΛ$, the symmetric $90\%$ credible interval of $\tildeΛ$ is estimated to be $481^{+436}_{-359}$ and $402^{+465}_{-279}$ for the case of $f_\mathrm{max}=1000$ and $2048~\mathrm{Hz}$, respectively, where $f_\mathrm{max}$ is the maximum frequency in the analysis. We also reanalyze the event with other waveform …
Effective-one-body (EOB) numerical-relativity (NR) waveform models for spin-aligned binary black holes (BBHs), known as the SEOBNR waveform models, are based on the EOB theoretical framework and NR simulations. SEOBNR models have played an important role in the LIGO scientific collaboration (LSC) gravitational wave (GW) data analysis for both signal search and parameter estimation. SEOBNR models for quasi-circular orbits have evolved through version 1 to version 4 by extending their validity domain and including more NR results. Along another direction, we recently extended SEOBNRv1 model to S…
A present challenge in testing general relativity (GR) with binary black hole gravitational wave detections is the inability to perform model-dependent tests due to the lack of merger waveforms in beyond-GR theories. In this study, we produce the first numerical relativity binary black hole gravitational waveform in Einstein dilaton Gauss-Bonnet (EDGB) gravity, a higher-curvature theory of gravity with motivations in string theory. We evolve a binary black hole system in order-reduced EDGB gravity, with parameters consistent with GW150914. We focus on the merger portion of the waveform, due to…
We introduce a method to quantify the initial eccentricity, gravitational wave frequency, and mean anomaly of numerical relativity simulations that describe non-spinning black holes on moderately eccentric orbits. We demonstrate that this method provides a robust characterization of eccentric binary black hole mergers with mass-ratios $q\leq10$ and eccentricities $e_0\leq0.2$ fifteen cycles before merger. We quantify the circularization rate of a variety of eccentric numerical relativity waveforms introduced in [1] by computing overlaps with their quasi-circular counterparts, finding that $50M…
We construct closed-form gravitational waveforms (GWs) with tidal effects for the coalescence and merger of binary neutron stars. The method relies on a new set of eccentricity-reduced and high-resolution numerical relativity (NR) simulations and is composed of three steps. First, tidal contributions to the GW phase are extracted from the time-domain NR data. Second, those contributions are employed to fix high-order coefficients in an effective and resummed post-Newtonian expression. Third, frequency-domain tidal approximants are built using the stationary phase approximation. Our tidal appro…
Gravitational wave observations of large mass ratio compact binary mergers like GW190814 highlight the need for reliable, high-accuracy waveform templates for such systems. We present NRHybSur2dq15, a new surrogate model trained on hybridized numerical relativity (NR) waveforms with mass ratios $q\leq15$, and aligned spins $|χ_{1z}|\leq0.5$ and $χ_{2z}=0$. We target the parameter space of GW190814-like events as large mass ratio NR simulations are very expensive. The model includes the (2,2), (2,1), (3,3), (4,4), and (5,5) spin-weighted spherical harmonic modes, and spans the entire LIGO bandw…
The recent observation of GW190412, the first high-mass ratio binary black-hole (BBH) merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using \texttt{NRSur7dq4}, a recently developed numerical relativity waveform surrogate model that includes all $\ell \leq 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants …
Gravitational-wave parameter estimation is only as good as the theory the waveform generation models are based upon. It is therefore crucial to test General Relativity (GR) once data becomes available. Many previous works, such as studies connected with the ppE framework by Yunes and Pretorius, rely on the stationary phase approximation (SPA) to model deviations from GR in the frequency domain. As Fast Fourier Transform algorithms have become considerably faster and in order to circumvent possible problems with the SPA, we test GR with corrected time domain waveforms instead of SPA waveforms. …
We determine the mass-ratio, eccentricity and binary inclination angles that maximize the contribution of the higher-order waveform multipoles $(\ell, \, |m|)= \{(2,\,2),\, (2,\,1),\, (3,\,3),\, (3,\,2), \, (3,\,1),\, (4,\,4),\, (4,\,3),\, (4,\,2),\,(4,\,1)\}$ for the gravitational wave detection of eccentric binary black hole mergers. We carry out this study using numerical relativity waveforms that describe non-spinning black hole binaries with mass-ratios $1\leq q \leq 10$, and orbital eccentricities as high as $e_0=0.18$ fifteen cycles before merger. For stellar-mass, asymmetric mass-ratio…
Binary black hole systems are among the most important sources for gravitational wave detection. And also they are good objects for theoretical research for general relativity. Gravitational waveform template is important to data analysis. Effective-one-body-numerical-relativity (EOBNR) model has played an essential role in the LIGO data analysis. For future space-based gravitational wave detection, many binary systems will admit somewhat orbit eccentricity. At the same time the eccentric binary is also an interesting topic for theoretical study in general relativity. In this paper we construc…
Observation and characterisation of gravitational waves from binary black holes requires accurate knowledge of the expected waveforms. The late inspiral and merger phase of the waveform is obtained through direct numerical integration of the full 3-dimensional Einstein equations. The Spectral Einstein Code (SpEC) utilizes a multi-domain pseudo-spectral method tightly adapted to the geometry of the black holes; it is computationally efficient and accurate, but--for high mass-ratios and large spins--sometimes requires manual fine-tuning for the merger-phase of binaries. The Einstein Toolkit (ET)…
We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to no…
Motivated by the parameterized post-Einsteinian (ppE) scheme devised by Yunes and Pretorius, which introduces corrections to the post-Newtonian coefficients of the frequency domain gravitational waveform in order to emulate alternative theories of gravity, we compute analytical time domain waveforms that, after a numerical Fourier transform, aim to represent (phase corrected only) ppE waveforms. In this formalism, alternative theories manifest themselves via corrections to the phase and frequency, as predicted by General Relativity (GR), at different post-Newtonian (PN) orders. In order to pre…
Impact of numerical-relativity waveform calibration on parametrized post-Einsteinian tests
The Grainger College of Engineering, Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格拉尼格工程学院、宇宙高级研究中心及物理系）；Department of Physics and Astronomy, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校物理与天文学系）；Nevada Center for Astrophysics, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校内华达天体物理学中心）
Observations of gravitational waves (GWs) from compact binary coalescences provide powerful tests of general relativity (GR), but systematic errors in data analysis could lead to incorrect scientific conclusions. This issue is especially serious in the third-generation GW detectors in which the signal-to-noise ratio (SNR) is high and the number of detections is large. In this work, we investigate the impacts of overlapping signals and inaccurate waveform models on tests of GR. We simulate mock catalogs for Einstein Telescope and Cosmic Explorer and perform parametric tests of GR using waveform…
We present the first surrogate model for gravitational waveforms from the coalescence of precessing binary black holes. We call this surrogate model NRSur4d2s. Our methodology significantly extends recently introduced reduced-order and surrogate modeling techniques, and is capable of directly modeling numerical relativity waveforms without introducing phenomenological assumptions or approximations to general relativity. Motivated by GW150914, LIGO's first detection of gravitational waves from merging black holes, the model is built from a set of $276$ numerical relativity (NR) simulations with…
We present the first numerical-relativity simulation of a compact-object binary whose gravitational waveform is long enough to cover the entire frequency band of advanced gravitational-wave detectors, such as LIGO, Virgo and KAGRA, for mass ratio 7 and total mass as low as $45.5\,M_\odot$. We find that effective-one-body models, either uncalibrated or calibrated against substantially shorter numerical-relativity waveforms at smaller mass ratios, reproduce our new waveform remarkably well, with a negligible loss in detection rate due to modeling error. In contrast, post-Newtonian inspiral wavef…
We present the Computational Relativity CoRe collaboration's public database of gravitational waveforms from binary neutron star mergers. The database currently contains 367 waveforms from numerical simulations that are consistent with general relativity and that employ constraint satisfying initial data in hydrodynamical equilibrium. It spans 164 physically distinct configuration with different binary parameters (total binary mass, mass-ratio, initial separation, eccentricity, and stars' spins) and simulated physics. Waveforms computed at multiple grid resolutions and extraction radii are pro…
We construct a new factorized waveform including $(l,|m|)=(2,2),(2,1),(3,3),(4,4)$ modes based on effective-one-body (EOB) formalism, which is valid for spinning binary black holes (BBH) in general equatorial orbit. When combined with the dynamics of $\texttt{SEOBNRv4}$, the $(l,|m|)=(2,2)$ mode waveform generated by this new waveform can fit the original $\texttt{SEOBNRv4}$ waveform very well in the case of a quasi-circular orbit. We have calibrated our new waveform model to the Simulating eXtreme Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in $(20,200)M_\odot$ us…
Analytic One-loop Scattering Waveform in General Relativity
Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay（理论物理研究所，法国原子能与替代能源委员会，法国国家科学研究中心，巴黎萨克雷大学）；Dipartimento di Fisica e Astronomia, Università degli Studi di Padova and INFN Sezione di Padova（帕多瓦大学物理与天文系，意大利国家核物理研究院帕多瓦分部）
Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the signals expected to be produced by a range of astrophysical systems, such as binary black holes. These waveform signals can be computed using numerical relativity techniques, where the Einstein field equations are solved numerically, and the signal is extracted from the simulation. Numerical relativity simulations are, however, computationally expensive, lead…
During binary black hole (BBH) mergers, energy and momenta are carried away from the binary system as gravitational radiation. Access to the radiated energy and momenta allows us to predict the properties of the remnant black hole. We develop a Python package gw_remnant to compute the remnant mass, remnant spin, peak luminosity, and the final kick imparted on the remnant black hole from the gravitational radiation. Using this package, we compute the remnant properties of the final black hole in case of non-spinning BBH mergers with mass ratios ranging from q=2.5 to q=1000 using waveform modes …
Towards long and accurate numerical relativity waveforms of binary black holes beyond general relativity
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））；Cornell University（康奈尔大学）；California State University Fullerton（加州州立大学富勒顿分校）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；California Institute of Technology（加州理工学院）
Numerical relativity (NR) simulations provide the most accurate binary black hole gravitational waveforms, but are prohibitively expensive for applications such as parameter estimation. Surrogate models of NR waveforms have been shown to be both fast and accurate. However, NR-based surrogate models are limited by the training waveforms' length, which is typically about 20 orbits before merger. We remedy this by hybridizing the NR waveforms using both post-Newtonian and effective one body waveforms for the early inspiral. We present NRHybSur3dq8, a surrogate model for hybridized nonprecessing n…
Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from non-spinning BBH coalescences with mass ratios in $[1, 10]$ and durations corresponding to about $15$ orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms {\em not} used for the surrogate's training wit…
This document describes the new Numerical Relativity (NR) injection infrastructure in the LIGO Algorithms Library (LAL), which henceforth allows for the usage of NR waveforms as a discrete waveform approximant in LAL. With this new interface, NR waveforms provided in the described format can directly be used as simulated GW signals ("injections") for data analyses, which include parameter estimation, searches, hardware injections etc. As opposed to the previous infrastructure, this new interface natively handles sub-dominant modes and waveforms from numerical simulations of precessing binary b…
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…
