Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20 and 200M ⊙ , the effective-one-body nonprecessing (dominant mode) waveforms have overlap above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. We also show that-without further calibration-the precessing effective-onebody (dominant mode) waveforms have overlap above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time.

This paper presents a publicly available catalog of 174 numerical binary black-hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to 8:1, orbital eccentricities from a few percent to 10 −5 , black-hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.

We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal mode frequencies presented in a recent paper [1]. One set of modes, that we call "zerodamping modes", has vanishing imaginary part in the extremal limit, and exists for all corotating perturbations (i.e., modes with azimuthal index m ≥ 0). The other set (the "damped modes") retains a finite decay rate even for extremal Kerr black holes, and exists only for a subset of corotating modes. As the angular momentum approaches its extremal value, the frequency spectrum bifurcates into these two distinct branches when both types of modes are present. We discuss the physical reason for the mode branching by developing and using a bound-state formulation for the perturbations of generic Kerr black holes. We also numerically explore the specific case of the fundamental l = 2 modes, which have the greatest astrophysical interest. Using the results of these investigations, we compute the quasinormal mode response of a nearly extremal Kerr black hole to perturbations. We show that many superimposed overtones result in a slow power-law decay of the quasinormal ringing at early times, which later gives way to exponential decay. This exceptional early-time power-law decay implies that the ringdown phase is long-lived for black holes with large angular momentum, which could provide a promising strong source for gravitational-wave detectors.

A useful choice of gauge when including null infinity in the computational domain is scri-fixing, that is, fixing the spatial coordinate location of null infinity. This choice allows us to avoid the introduction of artificial timelike outer boundaries in numerical calculations. We construct manifestly stationary scri-fixing coordinates explicitly on Minkowski, Schwarzschild and Kerr spacetimes.PACS numbers: 04.20.Dm, 04.25.Ha, 04.20.Jb MotivationIn numerical studies of the initial value problem for test fields on asymptotically flat background spacetimes, one typically truncates the solution domain by introducing an artificial timelike outer boundary into the spacetime. The solution then is calculated on a finite, spatially compact domain. The boundary of this domain is not part of the physical problem. Therefore, one tries to construct boundary conditions that correspond to transparency of this artificial outer boundary. In addition, these boundary conditions are required to form a well-posed initial boundary value problem (IBVP).In general, it is not possible to construct such boundary conditions. Spurious reflections occur from the outer boundary even for the simple case of the flat wave equation on a threedimensional ball [50]. One therefore tries to minimize the amount of such spurious reflections in a manner that also ensures the well-posedness of the IBVP. Such boundary conditions are called non-reflecting or absorbing. It is, however, very difficult to construct them when the curvature of the background does not vanish or when nonlinear terms appear in the equations. One needs to account for backscatter off curvature or self-interaction of the field near the boundary. A bad choice of boundary data can destroy relevant features of the solution. It has been shown, for example, that a certain choice of boundary data, commonly used in numerical relativity, destroys the polynomial tail behavior of solutions to wave equations on a Schwarzschild spacetime [8].

The Numerical–Relativity–Analytical–Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ∼100–200M⊙, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios ⩽4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

We compute and analyze the gravitational waveform emitted to future null infinity by a system of two black holes in the large-mass-ratio limit. We consider the transition from the quasiadiabatic inspiral to plunge, merger, and ringdown. The relative dynamics is driven by a leading order in the mass ratio, 5PN-resummed, effective-one-body (EOB), analytic-radiation reaction. To compute the waveforms, we solve the Regge-Wheeler-Zerilli equations in the time-domain on a spacelike foliation, which coincides with the standard Schwarzschild foliation in the region including the motion of the small black hole, and is globally hyperboloidal, allowing us to include future null infinity in the computational domain by compactification. This method is called the hyperboloidal layer method, and is discussed here for the first time in a study of the gravitational radiation emitted by black hole binaries. We consider binaries characterized by five mass ratios, ¼ 10 À2;À3;À4;À5;À6 , that are primary targets of space-based or thirdgeneration gravitational wave detectors. We show significative phase differences between finite-radius and null-infinity waveforms. We test, in our context, the reliability of the extrapolation procedure routinely applied to numerical relativity waveforms. We present an updated calculation of the final and maximum gravitational recoil imparted to the merger remnant by the gravitational wave emission, v end kick =ðc 2 Þ ¼ 0:04474 AE 0:00007 and v max kick =ðc 2 Þ ¼ 0:05248 AE 0:00008. As a self-consistency test of the method, we show an excellent fractional agreement (even during the plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the gravitational wave angular momentum flux computed at null infinity. New results concerning the radiation emitted from unstable circular orbits are also presented. The high accuracy waveforms computed here could be considered for the construction of template banks or for calibrating analytic models such as the effective-one-body model.

Abstract. We present a new approach to solve the 2+1 Teukolsky equation for gravitational perturbations of a Kerr black hole. Our approach relies on a new horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial compactification. In particular, we present a framework for waveform generation from point-particle perturbations. Extensive tests of a time domain implementation in the code Teukode are presented. The code can efficiently deliver waveforms at future null infinity. The accuracy and convergence of the waveforms' phase and amplitude is demonstrated.As a first application of the method, we compute the gravitational waveforms from inspiraling and coalescing black-hole binaries in the large-mass-ratio limit. The smaller mass black hole is modeled as a point particle whose dynamics is driven by an effective-one-body-resummed analytical radiation reaction force. We compare the analytical, mechanical angular momentum loss (computed using two different prescriptions) to the gravitational wave angular momentum flux. We find that higher-order post-Newtonian corrections are needed to improve the consistency for rapidly spinning binaries. We characterize the multipolar waveform as a function of the black-hole spin. Close to merger, the subdominant multipolar amplitudes (notably the m = 0 ones) are enhanced for retrograde orbits with respect to prograde ones. We argue that this effect mirrors nonnegligible deviations from circularity of the dynamics during the late-plunge and merger phase. For the first time, we compute the gravitational wave energy flux flowing into the black hole during the inspiral using a time-domain formalism proposed by Poisson.Finally, a self-consistent, iterative method to compute the gravitational wave fluxes at leading-order in the mass of the particle is developed. The method can be used alternatively to the analytical radiation reaction in cases the analytical information is poor or not sufficient. Specifically, we apply it to compute dynamics and waveforms for a rapidly rotating black hole with dimensionless spin parameter a = +0.9. For this case, the simulation with the consistent flux differs from the one with the analytical flux by ∼ 35 gravitational wave cycles over a total of about 250 cycles. In this simulation the horizon absorption accounts for about +5 gravitational wave cycles.

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses µ and M in the extreme-mass-ratio limit, µ/M = ν ≪ 1. We focus on the transition from quasicircular inspiral to plunge, merger and ringdown. We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by leading-order O(ν) analytically-resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about 5 × 10 −4 rad and maintain then a remarkably accurate phase coherence during the long inspiral (∼ 33 orbits), accumulating only about −2 × 10 −3 rad until the last stable orbit, i.e. ∆φ/φ ∼ −5.95 × 10 −6 . We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as ±0.015 rad, with a fractional amplitude agreement of 2.5%. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.