Search

The behavior of merging black holes (including the emitted gravitational waves and the properties of the remnant) can currently be computed only by numerical simulations. This paper introduces ten numerical relativity simulations of binary black holes with equal masses and equal spins aligned or antialigned with the orbital angular momentum. The initial spin magnitudes have |Xi| ≤ 0.95 and are more concentrated in the aligned direction because of the greater astrophysical interest of this case. We combine these data with five previously reported simulations of the same configuration, but with different spin magnitudes, including the highest spin simulated to date, Xi ≈ 0.97. This data set is sufficiently accurate to enable us to offer improved analytic fitting formulas for the final spin and for the energy radiated by gravitational waves as a function of initial spin. The improved fitting formulas can help to improve our understanding of the properties of binary black hole merger remnants and can be used to enhance future approximate waveforms for gravitational wave searches, such as effective-one-body waveforms. [ABSTRACT FROM AUTHOR]

Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is not explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using superposed Kerr-Schild initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δɸ≲10-2 radians and the amplitudes agree to within δA/A ≲ 5 X 10-3, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in 105. [ABSTRACT FROM AUTHOR]

Numerical simulations of binary black holes--an important predictive tool for the detection of gravitational waves--are computationally expensive, especially for binaries with high mass ratios or with rapidly spinning constituent holes. Existing codes for evolving binary black holes rely on explicit time-stepping methods, for which the time-step size is limited by the smallest spatial scale through the Courant-Friedrichs-Lewy condition. Binary inspiral typically involves spatial scales (the spatial resolution required by a small or rapidly spinning hole) which are orders of magnitude smaller than the relevant (orbital, precession, and radiation-reaction) time scales characterizing the inspiral. Therefore, in explicit evolutions of binary black holes, the time-step size is typically orders of magnitude smaller than the relevant physical time scales. Implicit time-stepping methods allow for larger time steps, and they often reduce the total computational cost (without significant loss of accuracy) for problems dominated by spatial rather than temporal error, such as for binary-black-hole inspiral in corotating coordinates. However, fully implicit methods can be difficult to implement for nonlinear evolution systems like the Einstein equations. Therefore, in this paper we explore implicit-explicit (IMEX) methods and use them for the first time to evolve black-hole spacetimes. Specifically, as a first step toward IMEX evolution of a full binary-black-hole spacetime, we develop an IMEX algorithm for the generalized harmonic formulation of the Einstein equations and use this algorithm to evolve stationary and perturbed single-black-hole spacetimes. Numerical experiments explore the stability and computational efficiency of our method. [ABSTRACT FROM AUTHOR]

Astrophysically realistic black holes may have spins that are nearly extremal (i.e., close to 1 in dimensionless units). Numerical simulations of binary black holes are important tools both for calibrating analytical templates for gravitational-wave detection and for exploring the nonlinear dynamics of curved spacetime. However, all previous simulations of binary-black-hole inspiral, merger, and ringdown have been limited by an apparently insurmountable barrier: the merging holes' spins could not exceed 0.93, which is still a long way from the maximum possible value in terms of the physical effects of the spin. In this paper, we surpass this limit for the first time, opening the way to explore numerically the behavior of merging, nearly extremal black holes. Specifically, using an improved initial-data method suitable for binary black holes with nearly extremal spins, we simulate the inspiral (through 12.5 orbits), merger and ringdown of two equal-mass black holes with equal spins of magnitude 0.95 antialigned with the orbital angular momentum. [ABSTRACT FROM AUTHOR]

Characterizing the properties of black holes is one of the most important science objectives for gravitational-wave observations. Astrophysical evidence suggests that black holes that are nearly extremal (i.e., spins near the theoretical upper limit) might exist and, thus, might be among the merging black holes observed with gravitational waves. In this paper, we explore how well current gravitational wave parameter estimation methods can measure the spins of rapidly spinning black holes in binaries. We simulate gravitational-wave signals using numerical-relativity waveforms for nearly-extremal, merging black holes. For simplicity, we confine our attention to binaries with spins parallel or antiparallel with the orbital angular momentum. We find that recovering the holes' nearly extremal spins is challenging. When the spins are nearly extremal and parallel to each other, the resulting parameter estimates do recover spins that are large, though the recovered spin magnitudes are still significantly smaller than the true spin magnitudes. When the spins are nearly extremal and antiparallel to each other, the resulting parameter estimates recover the small effective spin but incorrectly estimate the individual spins as nearly zero. We study the effect of spin priors and argue that a commonly used prior (uniform in spin magnitude and direction) hinders unbiased recovery of large black-hole spins. [ABSTRACT FROM AUTHOR]

The behavior of merging black holes (including the emitted gravitational waves and the properties of the remnant) can currently be computed only by numerical simulations. This paper introduces ten numerical relativity simulations of binary black holes with equal masses and equal spins aligned or antialigned with the orbital angular momentum. The initial spin magnitudes have |i|0.95 and are more concentrated in the aligned direction because of the greater astrophysical interest of this case. We combine these data with five previously reported simulations of the same configuration, but with different spin magnitudes, including the highest spin simulated to date, i0.97. This data set is sufficiently accurate to enable us to offer improved analytic fitting formulas for the final spin and for the energy radiated by gravitational waves as a function of initial spin. The improved fitting formulas can help to improve our understanding of the properties of binary black hole merger remnants and can be used to enhance future approximate waveforms for gravitational wave searches, such as effective-one-body waveforms. [ABSTRACT FROM AUTHOR]

Initial data for numerical evolutions of binary-black holes have been dominated by “conformally flat” (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated “conformally curved” initial data (i.e., initial data in which the background metric is not explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using superposed Kerr-Schild initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δϕ≲10-2 radians and the amplitudes agree to within δA/A≲5×10-3, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in 105. [ABSTRACT FROM AUTHOR]

Coalescing binaries of neutron stars and black holes are one of the most important sources of gravitational waves for the upcoming network of ground-based detectors. Detection and extraction of astrophysical information from gravitational-wave signals requires accurate waveform models. The effective-one-body and other phenomenological models interpolate between analytic results and numerical relativity simulations, that typically span O(10) orbits before coalescence. In this paper we study the faithfulness of these models for neutron star-black hole binaries. We investigate their accuracy using new numerical relativity (NR) simulations that span 36-88 orbits, with mass ratios q and black hole spins j BH of (q,Xbh) = (7, ±0.4), (7, ±0.6), and (5, -0.9). These simulations were performed treating the neutron star as a low-mass black hole, ignoring its matter effects. We find that (i) the recently published SEOBNRvl and SEOBNRv2 models of the effective-one-body family disagree with each other (mismatches of a few percent) for black hole spins XBH ≥ 0.5 or XBH ≤ -0.3, with waveform mismatch accumulating during early inspiral; (ii) comparison with numerical waveforms indicates that this disagreement is due to phasing errors of SEOBNRvl, with SEOBNRv2 in good agreement with all of our simulations; (iii) phenomenological waveforms agree with SEOBNRv2 only for comparable-mass low-spin binaries, with overlaps below 0.7 elsewhere in the neutron star-black hole binary parameter space; (iv) comparison with numerical waveforms shows that most of this model's dephasing accumulates near the frequency interval where it switches to a phenomenological phasing prescription; and finally (v) both SEOBNR and post-Newtonian models are effectual for neutron star-black hole systems, but post-Newtonian waveforms will give a significant bias in parameter recovery. Our results suggest that future gravitational-wave detection searches and parameter estimation efforts would benefit from using SEOBNRv2 waveform templates when focused on neutron star-black hole systems with q ≲ 7 and XBH ≈ [-0.9, +0.6]. For larger black hole spins and/or binary mass ratios, we recommend the models be further investigated as NR simulations in that region of the parameter space become available. [ABSTRACT FROM AUTHOR]

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 200AiQ, 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-one-body (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. [ABSTRACT FROM AUTHOR]

We study the general relativistic periastron advance in spinning black hole binaries on quasicircular orbits, with spins aligned or antialigned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a nonspinning particle orbiting a Kerr black hole of mass M and spin S=-0.5M², down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations. [ABSTRACT FROM AUTHOR]

We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasicircular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinning particles onto the dynamics of an effective spinning particle in a (deformed) Kerr spacetime, fully symmetrized with respect to the two-body masses and spins, and (ii) the resummation, in the test-particle limit, of all post-Newtonian corrections linear in the spin of the particle. In fact, even when only the leading spin post-Newtonian corrections are included in the effective-one-body spinning Hamiltonian but all the test-particle corrections linear in the spin of the particle are resummed we find very good agreement with the numerical results (within the numerical error for equal-mass binaries and discrepancies of at most I % for larger mass ratios). Furthermore, we specialize to the extreme mass-ratio limit and derive, using the equations of motion in the gravitational skeleton approach, analytical expressions for the periastron advance, the meridional Lense-Thirring precession and spin precession frequency in the case of a spinning particle on a nearly circular equatorial orbit in Kerr spacetime, including also terms quadratic in the spin. [ABSTRACT FROM AUTHOR]

In recent papers, we and colleagues have introduced a way to visualize the full vacuum Riemann curvature tensor using frame-drag vortex lines and their vorticities, and tidal tendex lines and their tendicities. We have also introduced the concepts of horizon vortexes and tendexes and three-dimensional vortexes and tendexes (regions on or outside the horizon where vorticities or tendicities are large). In this paper, using these concepts, we discover a number of previously unknown features of quasinormal modes of Schwarzschild and Kerr black holes. These modes can be classified by a radial quantum number n, spheroidal harmonic orders (l, m), and parity, which can be electric [(-- 1)l+1] or magnetic [(--1)l+1]. Among our discoveries are these: (i) There is a near duality between modes of the same (n, l, m): a duality in which the tendex and vortex structures of electric-parity modes are interchanged with the vortex and tendex structures (respectively) of magnetic-parity modes, (ii) This near duality is perfect for the modes' complex eigenfrequencies (which are well known to be identical) and perfect on the horizon; it is slightly broken in the equatorial plane of a nonspinning hole, and the breaking becomes greater out of the equatorial plane, and greater as the hole is spun up; but even out of the plane for fast-spinning holes, the duality is surprisingly good, (iii) Electric-parity modes can be regarded as generated by three-dimensional tendexes that stick radially out of the horizon. As these "longitudinal," near-zone tendexes rotate or oscillate, they generate longitudinal-transverse near-zone vortexes and tendexes and outgoing and ingoing gravitational waves. The ingoing waves act back on the longitudinal tendexes, driving them to slide off the horizon, which results in decay of the mode's strength, (iv) By duality, magnetic-parity modes are driven in this same manner by longitudinal, near-zone vortexes that stick out of the horizon, (v) When visualized, the three-dimensional vortexes and tendexes of a (l, m) = (2,2) mode, and also a (2,1) mode, spiral outward and backward like water from a whirling sprinkler, becoming outgoing gravitational waves. By contrast, a (2,2) mode superposed on a (2, --2) mode, has oscillating horizon vortexes or tendexes that eject three-dimensional vortexes and tendexes, which propagate outward becoming gravitational waves; and so does a (2,0) mode, (vi) For magnetic-parity modes of a Schwarzschild black hole, the perturbative frame-drag field, and hence also the perturbative vortexes and vortex lines, are strictly gauge invariant (unaffected by infinitesimal magnetic-parity changes of time slicing and spatial coordinates), (vii) We have computed the vortex and tendex structures of electric-parity modes of Schwarzschild in two very different gauges and find essentially no discernible differences in their pictorial visualizations, (viii) We have compared the vortex lines, from a numerical-relativity simulation of a black hole binary in its final ringdown stage, with the vortex lines of a (2,2) electric-parity mode of a Kerr black hole with the same spin (a/M = 0.945) and find remarkably good agreement. [ABSTRACT FROM AUTHOR]

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field ε, which produces tidal forces, and the frame-drag field B, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of ε) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes' horizon tendicity and vorticity (the normal-normal components of ε and B on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon's intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities(ε,B, the tendex lines and vortex lines, the lines' tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. We also explore how the tendex and vortex lines change as the spin of a black hole is increased, and we find, for example, that as a black hole is spun up through a dimensionless spin a/M = √3/2, the horizon tendicity at its poles changes sign, and an observer hovering or falling inward there switches from being stretched radially to being squeezed. At this spin, the tendex lines that stick out from the horizon's poles switch from reaching radially outward toward infinity to emerging from one pole, swinging poloidally around the hole and descending into the other pole. [ABSTRACT FROM AUTHOR]

We investigate the suitability and properties of a quasi-Kinnersley tetrad and a geometrically motivated coordinate system as tools for quantifying both strong-field and wave-zone effects in numerical relativity (NR) simulations. We fix two of the coordinate degrees of freedom of the metric, namely, the radial and latitudinal coordinates, using the Coulomb potential associated with the quasi-Kinnersley transverse frame. These coordinates are invariants of the spacetime and can be used to unambiguously fix the outstanding spin-boost freedom associated with the quasi-Kinnersley frame (and thus can be used to choose a preferred quasi-Kinnersley tetrad). In the limit of small perturbations about a Kerr spacetime, these geometrically motivated coordinates and quasi-Kinnersley tetrad reduce to Boyer-Lindquist coordinates and the Kinnersley tetrad, irrespective of the simulation gauge choice. We explore the properties of this construction both analytically and numerically, and we gain insights regarding the propagation of radiation described by a super-Poynting vector, further motivating the use of this construction in NR simulations. We also quantify in detail the peeling properties of the chosen tetrad and gauge. We argue that these choices are particularly well-suited for a rapidly converging wave-extraction algorithm as the extraction location approaches infinity, and we explore numerically the extent to which this property remains applicable on the interior of a computational domain. Using a number of additional tests, we verify numerically that the prescription behaves as required in the appropriate limits regardless of simulation gauge; these tests could also serve to benchmark other wave extraction methods. We explore the behavior of the geometrically motivated coordinate system in dynamical binary-black-hole NR mergers; while we obtain no unexpected results, we do find that these coordinates turn out to be useful for visualizing NR simulations (for example, for vividly illustrating effects such as the initial burst of spurious junk radiation passing through the computational domain). Finally, we carefully scrutinize the head-on collision of two black holes and, for example, the way in which the extracted waveform changes as it moves through the computational domain. [ABSTRACT FROM AUTHOR]

This paper presents a tunable effective-one-body (EOB) model for black-hole (BH) binaries of arbitrary mass ratio and aligned spins. This new EOB model incorporates recent results of small-mass-ratio simulations based on Teukolsky's perturbative formalism. The free parameters of the model are calibrated to numerical-relativity simulations of nonspinning BH-BH systems of five different mass ratios and to equal-mass nonprecessing BH-BH systems with dimensionless BH spins χi ≃ ±0.44. The present analysis focuses on the orbital dynamics of the resulting EOB model, and on the dominant (ℓ, m) = (2, 2) gravitational-wave mode. The calibrated EOB model can generate inspiral-merger-ringdown waveforms for nonprecessing, spinning BH binaries with any mass ratio and with individual BH spins -- 1 ≤ χi ≲ 0.7. Extremizing only over time and phase shifts, the calibrated EOB model has overlaps larger than 0.997 with each of the seven numerical-relativity waveforms for total masses between 20Mo and 2OOM0, using the Advanced LIGO noise curve. We compare the calibrated EOB model with two additional equal-mass highly spinning (χi ≤ --0.95, +0.97) numerical-relativity waveforms, which were not used during calibration. We find that the calibrated model has an overlap larger than 0.995 with the simulation with nearly extremal ant ¡aligned spins. Extension of this model to black holes with aligned spins x¡ --0.7 requires improvements of our modeling of the plunge dynamics and inclusion of higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force. [ABSTRACT FROM AUTHOR]

When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Ricmann tensor) gets split into two spatial, symmetric, and trace-free tensors: (i) the Weyl tensor's so-called electric part or tidal field ∊jk, which raises tides on the Earth's oceans and drives geodesic deviation (the relative acceleration of two freely falling test particles separated by a spatial vector &xgr; is δaj = --∊jk&xgr;k), and (ii) the Weyl tensor's so-called magnetic part or (as we call it) frame-drag field Bjk, which drives differential frame dragging (the precessional angular velocity of a gyroscope at the tip of &xgr;, as measured using a local inertial frame at the tail of &xgr; is δΩj = Bjk&xgr;k). Being symmetric and trace-free, ∊jk and Bjk each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of ∊jk eigenvectors tidal tendex lines or simply tendex lines, we call each tendex line's eigenvalue its tendicity. and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for "B¡k are frame-drag vortex lines or simply vortex lines, their vorticities, and their vortexes. These concepts are powerful tools for visualizing spacetime curvature. We build up physical intuition into them by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side-by-side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. We show that a rotating current quadrupole has four rotating vortexes that sweep outward and backward like water streams from a rotating sprinkler. As they sweep, the vortexes acquire accompanying tendexes and thereby become outgoing current-quadrupole gravitational waves. We show similarly that a rotating mass quadrupole has four rotating, outward-and-backward sweeping tendexes that acquire accompanying vortexes as they sweep, and become outgoing mass-quadrupole gravitational waves. We show, further, that an oscillating current quadrupole ejects sequences of vortex loops that acquire accompanying tendex loops as they travel, and become current-quadrupole gravitational waves; and similarly for an oscillating mass quadrupole. And we show how a binary's tendex lines transition, as one moves radially, from those of two static point particles in the deep near zone, to those of a single spherical body in the outer part of the near zone and inner part of the wave zone (where the binary's mass monopole moment dominates), to those of a rotating quadrupole in the far wave zone (where the quadrupolar gravitational waves dominate). In Paper II we will use these vortex and tendex concepts to gain insight into the quasinormal modes of black holes, and in subsequent papers, by combining these concepts with numerical simulations, we will explore the nonlinear dynamics of curved spacetime around colliding black holes. We have published a brief overview of these applications in R. Owen et al., Phys. Rev. Lett. 106. 151101 (2011). We expect these vortex and tendex concepts to become powerful tools for general relativity research in a variety of topics. [ABSTRACT FROM AUTHOR]

In this work we study the dynamics of spinning binary black hole systems in the strong field regime. For this purpose we extract from numerical relativity simulations the binding energy, specific orbital angular momentum, and gauge-invariant frequency. The goal of our work is threefold: First, we extract the individual spin contributions to the binding energy, in particular the spin-orbit, spin-spin, and cubic-in-spin terms. Second, we compare our results with predictions from waveform models and find that while post-Newtonian approximants are not capable of representing the dynamics during the last few orbits before merger, there is good agreement between our data and effective-one-body approximants as well as the numerical relativity surrogate models. Finally, we present phenomenological representations for the binding energy for nonspinning systems with mass ratios up to q=10 and for the spin-orbit interaction for mass ratios up to q=8 obtaining accuracies of ≲0.1% and ≲6%, respectively. [ABSTRACT FROM AUTHOR]

Spin-orbit resonances have important astrophysical implications as the evolution and subsequent coalescence of supermassive black hole binaries in one of these configurations may lead to low recoil velocity of merger remnants. It has also been shown that black hole spins in comparable mass stellar-mass black hole binaries could preferentially lie in a resonant plane when their gravitational waves (GWs) enter the advanced LIGO frequency band [1]. Therefore, it is highly desirable to investigate the possibility of detection and subsequent characterization of such GW sources in the advanced detector era, which can, in turn, improve our perception of their high mass counterparts. The current detection pipelines involve only nonprecessing templates for compact binary searches whereas parameter estimation pipelines can afford to use approximate precessing templates. In this paper, we test the performance of these templates in detection and characterization of spin-orbit resonant binaries. We use fully precessing time-domain SEOBNRv3 waveforms as well as four numerical relativity (NR) waveforms to model GWs from spin-orbit resonant binaries and filter them through IMRPhenomD, SEOBNRv4 and IMRPhenomPv2 approximants. We find that the nonprecessing approximants IMRPhenomD and SEOBNRv4 recover only ~70% of injections with fitting factor (FF) higher than 0.97 (or 90% of injections with FF>0.9). This loss in signal-to-noise ratio is mainly due to the missing physics in these approximants in terms of precession and nonquadrupole modes. However, if we use a new statistic, i.e., maximizing the matched filter output over the sky-location parameters as well, the precessing approximant IMRPhenomPv2 performs magnificently better than their nonprecessing counterparts with recovering 99% of the injections with FFs higher than 0.97. Interestingly, injections with Δϕ=180° have higher FFs (Δϕ is the angle between the components of the black hole spins in the plane orthogonal to the orbital angular momentum) as compared to their Δϕ=0° and generic counterparts. This is because Δϕ=180° binaries are not as strongly precessing as Δϕ=0° and generic binaries. This implies that we will have a slight observation bias towards Δϕ=180° and away from Δϕ=0° resonant binaries while using nonprecessing templates for searches. Moreover, all template approximants are able to recover most of the injected NR waveforms with FFs >0.95. For all the injections including NR, the systematic error in estimating chirp mass remains below <10% with minimum error for Δϕ=180° resonant binaries. The symmetric mass-ratio can be estimated with errors below 15%. The effective spin parameter χeff is measured with maximum absolute error of 0.13. The in-plane spin parameter χp is mostly underestimated indicating that a precessing signal will be recovered as a relatively less precessing signal. Based on our findings, we conclude that we not only need improvements in waveform models towards precession and nonquadrupole modes but also better search strategies for precessing GW signals. [ABSTRACT FROM AUTHOR]

We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration toward larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness--at design Advanced-LIGO sensitivity--above 99% against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios ≳ 4 and double spin ≳ 0.8 will be crucial to resolving discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO. [ABSTRACT FROM AUTHOR]

We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasicircular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinning particles onto the dynamics of an effective spinning particle in a (deformed) Kerr spacetime, fully symmetrized with respect to the two-body masses and spins, and (ii) the resummation, in the test-particle limit, of all post-Newtonian corrections linear in the spin of the particle. In fact, even when only the leading spin post-Newtonian corrections are included in the effective-one-body spinning Hamiltonian but all the test-particle corrections linear in the spin of the particle are resummed we find very good agreement with the numerical results (within the numerical error for equal-mass binaries and discrepancies of at most 1% for larger mass ratios). Furthermore, we specialize to the extreme mass-ratio limit and derive, using the equations of motion in the gravitational skeleton approach, analytical expressions for the periastron advance, the meridional Lense-Thirring precession and spin precession frequency in the case of a spinning particle on a nearly circular equatorial orbit in Kerr spacetime, including also terms quadratic in the spin. [ABSTRACT FROM AUTHOR]

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field E, which produces tidal forces, and the frame-drag field B, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of E) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes’ horizon tendicity and vorticity (the normal-normal components of E and B on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon’s intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities (E, B, the tendex lines and vortex lines, the lines’ tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. We also explore how the tendex and vortex lines change as the spin of a black hole is increased, and we find, for example, that as a black hole is spun up through a dimensionless spin a/M=√3/2, the horizon tendicity at its poles changes sign, and an observer hovering or falling inward there switches from being stretched radially to being squeezed. At this spin, the tendex lines that stick out from the horizon’s poles switch from reaching radially outward toward infinity to emerging from one pole, swinging poloidally around the hole and descending into the other pole. [ABSTRACT FROM AUTHOR]

We investigate the suitability and properties of a quasi-Kinnersley tetrad and a geometrically motivated coordinate system as tools for quantifying both strong-field and wave-zone effects in numerical relativity (NR) simulations. We fix two of the coordinate degrees of freedom of the metric, namely, the radial and latitudinal coordinates, using the Coulomb potential associated with the quasi-Kinnersley transverse frame. These coordinates are invariants of the spacetime and can be used to unambiguously fix the outstanding spin-boost freedom associated with the quasi-Kinnersley frame (and thus can be used to choose a preferred quasi-Kinnersley tetrad). In the limit of small perturbations about a Kerr spacetime, these geometrically motivated coordinates and quasi-Kinnersley tetrad reduce to Boyer-Lindquist coordinates and the Kinnersley tetrad, irrespective of the simulation gauge choice. We explore the properties of this construction both analytically and numerically, and we gain insights regarding the propagation of radiation described by a super-Poynting vector, further motivating the use of this construction in NR simulations. We also quantify in detail the peeling properties of the chosen tetrad and gauge. We argue that these choices are particularly well-suited for a rapidly converging wave-extraction algorithm as the extraction location approaches infinity, and we explore numerically the extent to which this property remains applicable on the interior of a computational domain. Using a number of additional tests, we verify numerically that the prescription behaves as required in the appropriate limits regardless of simulation gauge; these tests could also serve to benchmark other wave extraction methods. We explore the behavior of the geometrically motivated coordinate system in dynamical binary-black-hole NR mergers; while we obtain no unexpected results, we do find that these coordinates turn out to be useful for visualizing NR simulations (for example, for vividly illustrating effects such as the initial burst of spurious junk radiation passing through the computational domain). Finally, we carefully scrutinize the head-on collision of two black holes and, for example, the way in which the extracted waveform changes as it moves through the computational domain. [ABSTRACT FROM AUTHOR]