Bowen-York trumpet data and black-hole simulations

The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a ``trumpet'' topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an outline of an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that for boosted trumpets the black-hole mass can be prescribed {\it a priori}, without recourse to the iterative procedure that is necessary for wormhole data.Comment: 15 pages, 14 figures. Published versio

Implementation of standard testbeds for numerical relativity

We discuss results that have been obtained from the implementation of the initial round of testbeds for numerical relativity which was proposed in the first paper of the Apples with Apples Alliance. We present benchmark results for various codes which provide templates for analyzing the testbeds and to draw conclusions about various features of the codes. This allows us to sharpen the initial test specifications, design a new test and add theoretical insight.Comment: Corrected versio

Beyond the Bowen-York extrinsic curvature for spinning black holes

It is well-known that Bowen-York initial data contain spurious radiation. Although this ``junk'' radiation has been seen to be small for non-spinning black-hole binaries in circular orbit, its magnitude increases when the black holes are given spin. It is possible to reduce the spurious radiation by applying the puncture approach to multiple Kerr black holes, as we demonstrate for examples of head-on collisions of equal-mass black-hole binaries.Comment: 10 pages, 2 figures, submitted to special "New Frontiers in Numerical Relativity" issue of Classical and Quantum Gravit

Retarded radiation from colliding black holes in the close limit

We use null hypersurface techniques in a new approach to calculate the retarded waveform from a binary black hole merger in the close approximation. The process of removing ingoing radiation from the system leads to two notable features in the shape of the close approximation waveform for a head-on collision of black holes: (i) an initial quasinormal ringup and (ii) weak sensitivity to the parameter controlling the collision velocity. Feature (ii) is unexpected and has the potential importance of enabling the design of an efficient template for extracting the gravitational wave signal from the noise

Total recoil: the maximum kick from nonspinning black-hole binary inspiral

When unequal-mass black holes merge, the final black hole receives a ``kick'' due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black hole inspirals. We study non-spinning black-hole binaries with mass ratios from $q=M_1/M_2=1$ to $q =0.25$ ($\eta = q/(1 + q)^2$ from 0.25 to 0.16). We accurately calculate the velocity of the kick to within 6%, and the final spin of the black holes to within 2%. A maximum kick of $175.2\pm11$ km s$^{-1}$ is achieved for $\eta = 0.195 \pm 0.005$.Comment: 4 pages, 4 figures. Version accepted by PR

Supermassive recoil velocities for binary black-hole mergers with antialigned spins

Recent calculations of the recoil velocity in binary black hole mergers have found the kick velocity to be of the order of a few hundred km/s in the case of non-spinning binaries and about $500$km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to $1300$km/s. We test these predictions and demonstrate that kick velocities of at least $2500$km/s are possible for equal-mass binaries with anti-aligned spins in the orbital plane. Kicks of that magnitude are likely to have significant repercussions for models of black-hole formation, the population of intergalactic black holes and the structure of host galaxies.Comment: Final version, published by Phys. Rev. Lett.; title changed according to suggestion of PRL; note added after preparation of manuscrip

Hyperboloidal evolution of test fields in three spatial dimensions

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.Comment: 10 pages, 8 figure

Exploring black hole superkicks

Recent calculations of the recoil velocity in black-hole binary mergers have found kick velocities of $\approx2500$km/s for equal-mass binaries with anti-aligned initial spins in the orbital plane. In general the dynamics of spinning black holes can be extremely complicated and are difficult to analyze and understand. In contrast, the ``superkick'' configuration is an example with a high degree of symmetry that also exhibits exciting physics. We exploit the simplicity of this ``test case'' to study more closely the role of spin in black-hole recoil and find that: the recoil is with good accuracy proportional to the difference between the $(l = 2, m = \pm 2)$ modes of $\Psi_4$, the major contribution to the recoil occurs within $30M$ before and after the merger, and that this is after the time at which a standard post-Newtonian treatment breaks down. We also discuss consequences of the $(l = 2, m = \pm 2)$ asymmetry in the gravitational wave signal for the angular dependence of the SNR and the mismatch of the gravitational wave signals corresponding to the north and south poles

Impact of gravitational radiation higher order modes on single aligned-spin gravitational wave searches for binary black holes

Current template-based gravitational wave searches for compact binary coalescences (CBC) use waveform models that neglect the higher order modes content of the gravitational radiation emitted, considering only the quadrupolar $(\ell,|m|)=(2,2)$ modes. We study the effect of such a neglection for the case of aligned-spin CBC searches for equal-spin (and non-spinning) binary black holes in the context of two versions of Advanced LIGO: the upcoming 2015 version, known as early Advanced LIGO (eaLIGO) and its Zero-Detuned High Energy Power version, that we will refer to as Advanced LIGO (AdvLIGO). In addition, we study the case of a non-spinning search for initial LIGO (iLIGO). We do this via computing the effectualness of the aligned-spin SEOBNRv1 ROM waveform family, which only considers quadrupolar modes, towards hybrid post-Newtonian/Numerical Relativity waveforms which contain higher order modes. We find that for all LIGO versions, losses of more than $10\%$ of events occur for mass ratio $q\geq6$ and $M \geq 100M_\odot$ due to the neglection of higher modes. Moreover, for iLIGO and eaLIGO, losses notably increase up to $(39,23)\%$ respectively for the highest mass $(220M_\odot)$ and mass ratio ($q=8$) studied. For the case of early AdvLIGO, losses of $10\%$ occur for $M>50M_\odot$ and $q\geq6$. Neglection of higher modes leads to observation-averaged systematic parameter biases towards lower spin, total mass and chirp mass. For completeness, we perform a preliminar, non-exhaustive comparison of systematic biases to statistical errors. We find that, for a given SNR, systematic biases dominate over statistical errors at much lower total mass for eaLIGO than for AdvLIGO

Gravitational waves from a fissioning white hole

We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger