We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on the BSSN formulation of Einstein's equations, when used with a 'pre-collapsed' initial lapse, is non-singular at the start of the evolution, and remains nonsingular and stable provided that a good choice is made for the gauge. As a test case, we use this technique to fully evolve orbiting black-hole binaries from near the Innermost Stable Circular Orbit (ISCO) regime. We show fourth order convergence of waveforms and compute the radiated gravitational energy and angular momentum from the plunge. These results are in good agreement with those predicted by the Lazarus approach.PACS numbers: 04.25. Dm, 04.25.Nx, 04.30.Db, 04.70.Bw One of the most significant goals of numerical relativity is to compute accurate gravitational waveforms from astrophysically realistic simulations of merging black-hole binaries. The expectation of very strong gravitational wave emission from the merger of two black holes, and some of the newest astrophysical observations, from supermassive galactic nuclei just about to merge [1] to stellar size black-hole binaries, make these systems one of the most extraordinary astrophysical objects under study today. Binary black hole mergers are expected not only to provide information about the history and formation of the binary system but also to provide important precise tests of strong-field, highly dynamical relativity.Motivated by the forthcoming observations of groundbased gravitational wave detectors, such as LIGO [2], and by the next generation of space-based detectors, such as LISA [3], the numerical relativity community has dedicated a great deal of effort to solving the binary-blackhole problem over the past few decades. After the 'Binary Black Hole Grand Challenge' [4] several new approaches have been pursued in the attempt to produce stable three-dimensional (3D) numerical codes capable of evolving the full Einstein field equations in the absence of any symmetry. This includes the introduction of new formulations of these equations and the development of numerical techniques for accurate evolutions of black-hole binaries, such as higher order finite differencing, spectral methods, and adaptive mesh refinement (AMR) (see Ref.[5] and references therein).The calculation of the gravitational radiation emitted from plunging black-hole binaries was pioneered through the use of the Lazarus approach, which bridges numerical relativity and perturbative techniques to extract approximate gravitational waveforms [6,7,8]. More recently important progress has been made toward evolving orbiting binary-black-hole spacetimes with the use of stable full 3D numerical relativity codes using corotating gauge conditions and singularity excision [9,10,11].Here we present a novel technique for evolving orbiting black holes based on puncture data. This technique does not ...

Recent calculations of gravitational radiation recoil generated during black-hole binary mergers have reopened the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy. Here we report the first systematic study of gravitational recoil of equal-mass binaries with equal, but counter-aligned, spins parallel to the orbital plane. Such an orientation of the spins is expected to maximize the recoil. We find that recoil velocity (which is perpendicular to the orbital plane) varies sinusoidally with the angle that the initial spin directions make with the initial linear momenta of each hole and scales up to a maximum of ∼ 4000 km s −1 for maximally-rotating holes. Our results show that the amplitude of the recoil velocity can depend sensitively on spin orientations of the black holes prior to merger. Introduction: Generic black-hole-binary mergers will display a rich spectrum of gravitational effects in the last few orbits prior to the formation of the single rotating remnant hole. These effects include spin and orbital plane precession, radiation of mass, linear and angular momentum, as well as spin-flips of the remnant horizon. Thanks to recent breakthroughs in the full non-linear numerical evolution of black-hole-binary spacetimes [1,2,3], it is now possible to accurately simulate the merger process and examine these effects in this highly non-linear regime [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Black-hole binaries will radiate between 2% and 8% of their total mass and up to 40% of their angular momenta, depending on the magnitude and direction of the spin components, during the merger [6,7,8]. In addition, the radiation of net linear momentum by a black-hole binary leads to the recoil of the final remnant hole [19,20,21,22,23,24,25,26,27,28]. This phenomenon can lead to astrophysically important effects [29,30].A non-spinning black-hole binary will emit net linear momentum parallel to its orbital plane if the individual holes have unequal masses. However, the maximum recoil in this case (which occurs when the mass ratio is q ≈ 0.36) is a relatively small ∼ 175 km s −1 [22].The first generic simulation of black-hole binaries with unequal masses and spins was reported in [24]. These black holes displayed spin precession and spin flips, and for the first time, recoil velocities over 400km s −1 , mostly along the orbital angular momentum direction. It was thus found that the unequal spin components to the recoil velocity can be much larger than those due to unequal masses, and that comparable mass, maximally spinning holes with spins in the orbital plane and counter-aligned

We report the first results from the evolution of generic black hole binaries, i.e., binaries containing unequalmass black holes with misaligned spins. Our configuration, which has a mass ratio of , consists of an initially 2 : 1 nonspinning hole orbiting a larger, rapidly spinning hole (specific spin ), with the spin direction a/m p 0.885 oriented Ϫ45Њ with respect to the orbital plane. We track the inspiral and merger for ∼2 orbits and find that the remnant receives a substantial kick of 454 km s Ϫ1 , more than twice as large as the maximum kick from nonspinning binaries. The remnant spin direction is flipped by 103Њ with respect to the initial spin direction of the larger hole. We performed a second run with antialigned spins, lying in the orbital plane that produces a kick a/m p ‫5.0ע‬ of ∼1830 km s Ϫ1 off the orbital plane. This value scales to nearly 4000 km s Ϫ1 for maximally spinning holes. Such a large recoil velocity opens up the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy.

We use the ''moving puncture'' approach to perform fully nonlinear evolutions of spinning quasicircular black-hole binaries with individual spins unaligned with the orbital angular momentum. We evolve configurations with the individual spins (parallel and equal in magnitude) pointing in the orbital plane and 45 above the orbital plane. We introduce a technique to measure the spin direction and track the precession of the spin during the merger, as well as measure the spin flip in the remnant horizon. The former configuration completes 1.75 orbits before merging, with the spin precessing by 98 and the final remnant horizon spin flipped by 72 with respect to the component spins. The latter configuration completes 2.25 orbits, with the spins precessing by 151 and the final remnant horizon spin flipped 34 with respect to the component spins. These simulations show for the first time how the spins are reoriented during the final stage of black-hole-binary mergers verifying the hypothesis of the spin-flip phenomenon.We also compute the track of the holes before merger and observe a precession of the orbital plane with frequency similar to the orbital frequency and amplitude increasing with time.

We have used our new technique for fully numerical evolutions of orbiting black-hole binaries without excision to model the last orbit and merger of an equal-mass black-hole system. We track the trajectories of the individual apparent horizons and find that the binary completed approximately one and a third orbits before forming a common horizon. Upon calculating the complete gravitational radiation waveform, horizon mass, and spin, we find that the binary radiated 3.2% of its mass and 24% of its angular momentum. The early part of the waveform, after a relatively short initial burst of spurious radiation, is oscillatory with increasing amplitude and frequency, as expected from orbital motion. The waveform then transitions to a typical 'plunge' waveform; i.e. a rapid rise in amplitude followed by quasinormal ringing. The plunge part of the waveform is remarkably similar to the waveform from the previously studied 'ISCO' configuration. We anticipate that the plunge waveform, when starting from quasicircular orbits, has a generic shape that is essentially independent of the initial separation of the binary.

We perform a set of 36 nonprecessing black-hole binary simulations with spins either aligned or counteraligned with the orbital angular momentum in order to model the final mass, spin, and recoil of the merged black hole as a function of the individual black hole spin magnitudes and the mass ratio of the progenitors. We find that the maximum recoil for these configurations is Vmax = 526 ± 23 km s −1 , which occurs when the progenitor spins are maximal, the mass ratio is qmax = m1/m2 = 0.623 ± 0.038, the smaller black-hole spin is aligned with the orbital angular momentum, and the larger black-hole spin is counteraligned (α1 = −α2 = 1). This maximum recoil is about 80 km s −1 larger than previous estimates, but most importantly, because the maximum occurs for smaller mass ratios, the probability for a merging binary to recoil faster than 400 km s −1 can be as large as 17%, while the probability for recoils faster than 250 km s −1 can be as large as 45%. We provide explicit phenomenological formulas for the final mass, spin, and recoil as a function of the individual BH spins and the mass difference between the two black holes. Here we include terms up through fourth-order in the initial spins and mass difference, and find excellent agreement (within a few percent) with independent results available in the literature. The maximum radiated energy is E rad /m ≈ 11.3% and final spin α max rem ≈ 0.952 for equal mass, aligned maximally spinning binaries.

We present a detailed description of techniques developed to combine 3D numerical simulations and, subsequently, a single black hole close-limit approximation. This method has made it possible to compute the first complete waveforms covering the post-orbital dynamics of a binary-black-hole system with the numerical simulation covering the essential nonlinear interaction before the close limit becomes applicable for the late time dynamics. In order to couple full numerical and perturbative methods we must address several questions. To determine when close-limit perturbation theory is applicable we apply a combination of invariant a priori estimates and a posteriori consistency checks of the robustness of our results against exchange of linear and nonlinear treatments near the interface. Our method begins with a specialized application of standard numerical techniques adapted to the presently realistic goal of brief, but accurate simulations. Once the numerically modeled binary system reaches a regime that can be treated as perturbations of the Kerr spacetime, we must approximately relate the numerical coordinates to the perturbative background coordinates. We also perform a rotation of a numerically defined tetrad to asymptotically reproduce the tetrad required in the perturbative treatment. We can then produce numerical Cauchy data for the close-limit evolution in the form of the Weyl scalar 4 and its time derivative ‫ץ‬ t 4 with both objects being first order coordinate and tetrad invariant. The Teukolsky equation in Boyer-Lindquist coordinates is adopted to further continue the evolution. To illustrate the application of these techniques we evolve a single Kerr hole and compute the spurious radiation as a measure of the error of the whole procedure. We also briefly discuss the extension of the project to make use of improved full numerical evolutions and outline the approach to a full understanding of astrophysical black-hole-binary systems which we can now pursue.

We explore the newly discovered "hangup-kick" effect, which greatly amplifies the recoil for configurations with partial spin-/ orbital-angular momentum alignment, by studying a set of 48 new simulations of equal-mass, spinning black-hole binaries. We propose a phenomenological model for the recoil that takes this new effect into account and then use this model, in conjunction with statistical distributions for the spin magnitude and orientations, based on accretion simulations, to find the probabilities for observing recoils of several thousand km s −1 . In addition, we provide initial parameters, eccentricities, radiated linear and angular momentum, precession rates and remnant mass, spin, and recoils for all 48 configurations. Our results indicate that surveys exploring peculiar (redshifted or blueshifted) differential line-of-sight velocities should observe at least one case above 2000 km s −1 out of four thousand merged galaxies. On the other hand, the probability that a remnant BH recoils in any direction at a velocity exceeding the ∼ 2000 km s −1 escape velocity of large elliptical galaxies is 0.03%. Probabilities of recoils exceeding the escape velocity quickly rise to 5% for galaxies with escape velocities of 1000 km s −1 and nearly 20% for galaxies with escape velocities of 500 km s −1 . In addition the direction of these large recoils is strongly peaked toward the angular momentum axis, with very low probabilities of recoils exceeding 350 km s −1 for angles larger than 45• with respect to the orbital angular momentum axis.