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

Binary black holes on a budget: Simulations using workstations

Binary black hole simulations have traditionally been computationally very expensive: current simulations are performed in supercomputers involving dozens if not hundreds of processors, thus systematic studies of the parameter space of binary black hole encounters still seem prohibitive with current technology. Here we show how the multi-layered refinement level code BAM can be used on dual processor workstations to simulate certain binary black hole systems. BAM, based on the moving punctures method, provides grid structures composed of boxes of increasing resolution near the center of the grid. In the case of binaries, the highest resolution boxes are placed around each black hole and they track them in their orbits until the final merger when a single set of levels surrounds the black hole remnant. This is particularly useful when simulating spinning black holes since the gravitational fields gradients are larger. We present simulations of binaries with equal mass black holes with spins parallel to the binary axis and intrinsic magnitude of S/m^2= 0.75. Our results compare favorably to those of previous simulations of this particular system. We show that the moving punctures method produces stable simulations at maximum spatial resolutions up to M/160 and for durations of up to the equivalent of 20 orbital periods.Comment: 20 pages, 8 figures. Final version, to appear in a special issue of Class. Quantum Grav. based on the New Frontiers in Numerical Relativity Conference, Golm, July 200

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

Radiation from low-momentum zoom-whirl orbits

We study zoom-whirl behaviour of equal mass, non-spinning black hole binaries in full general relativity. The magnitude of the linear momentum of the initial data is fixed to that of a quasi-circular orbit, and its direction is varied. We find a global maximum in radiated energy for a configuration which completes roughly one orbit. The radiated energy in this case exceeds the value of a quasi-circular binary with the same momentum by 15%. The direction parameter only requires minor tuning for the localization of the maximum. There is non-trivial dependence of the energy radiated on eccentricity (several local maxima and minima). Correlations with orbital dynamics shortly before merger are discussed. While being strongly gauge dependent, these findings are intuitive from a physical point of view and support basic ideas about the efficiency of gravitational radiation from a binary system.Comment: 9 pages, 6 figures, Amaldi8 conference proceedings as publishe

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

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

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.Comment: 11 pages, 6 figures, RevTeX

Homesteading the Plains: Toward a New History.

Through hard work and thorough research, Richard Edwards, Jacob Friefeld, and Rebecca Wingo seek to dispel any false notions and set the record straight on what was one of the most influential events in the history of the United States in their book, Homesteading the Plains. Th roughout the work, the authors are able to correct false historical accounts that cast a poor light on the Homestead Act while they provide a wealth of statistical evidence to move toward a new history, as the book’s subtitle suggests. Th e Homestead Act provided opportunity for many ancestors of current Great Plains residents and helped populate the Great Plains along with making the region a major agricultural producer, cementing our roles in both national and international markets. As land was given out, communities were formed and churches and schools were soon to follow, helping to make the region and its people not only economically viable, but also culturally significant. While nothing is without its flaws, the Homestead Act was successful in its original goals, which is conclusively proven throughout the book