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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]

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]

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 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]

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]

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]

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]