Numerical Evolution of Dynamic 3D Black Holes: Extracting Waves

We consider the numerical evolution of dynamic black hole initial data sets with a full 3D, nonlinear evolution code. These data sets consist of single black holes distorted by strong gravitational waves, and mimic the late stages of coalescing black holes. Through comparison with results from well established axisymmetric codes, we show that these dynamic black holes can be accurately evolved. In particular, we show that with present computational resources and techniques, the process of excitation and ringdown of the black hole can be evolved, and one can now extract accurately the gravitational waves emitted from the 3D Cartesian metric functions, even though they may be buried in the metric at levels on the order of $10^{-3}$ and below. Waveforms for both the $\ell=2$ and the much more difficult $\ell=4$ modes are computed and compared with axisymmetric calculations. In addition to exploring the physics of distorted black hole data sets, and showing the extent to which the waves can be accurately extracted, these results also provide important testbeds for all fully nonlinear numerical codes designed to evolve black hole spacetimes in 3D, whether they use singularity avoiding slicings, apparent horizon boundary conditions, or other evolution methods.Comment: 9 pages, 3 figures, LaTe

Three Dimensional Distorted Black Holes: Initial Data and Evolution

We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with adjustable distortion parameters in 3D. These data sets extend our existing test beds for 3D numerical relativity, representing the late stages of binary black hole collisions resulting from on-axis collision or 3D spiralling coalescence, and should provide insight into the physics of such systems. We describe the construction of these sets, the properties for a number of example cases, and report on progress evolving them.Comment: 3 pages, 2 postscript figures, LaTeX, uses mprocl.sty (available at http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the proceedings of the Marcel Grossmann 8 (Jerusalem, 1997

Three-dimensional simulations of distorted black holes; 1, Comparison with axisymmetric results

We consider the numerical evolution of black hole initial data sets, consisting of single black holes distorted by strong gravitational waves, with a full 3D, nonlinear evolution code. These data sets mimic the late stages of coalescing black holes. We compare various aspects of the evolution of axisymmetric initial data sets, obtained with this 3D code, to results obtained from a well established axisymmetric code. In both codes we examine and compare the behavior of metric functions, apparent horizon properties, and waveforms, and show that these dynamic black holes can be accurately evolved in 3D. In particular we show that with present computational resources and techniques, the process of excitation and ringdown of the black hole can be evolved, and one can now extract accurately the gravitational waves emitted from the 3D Cartesian metric functions, even when they carry away only a small fraction ($<< 1$) of the rest mass energy of the system. Waveforms for both the and compared with axisymmetric calculations. In addition to exploring the physics of distorted black hole data sets, and showing the extent to which the waves can be accurately extracted, these results also provide important testbeds for all fully nonlinear numerical codes designed to evolve black hole spacetimes in 3D, whether they use singularity avoiding slicings, apparent horizon boundary conditions, or other evolution methods

Binary Black Hole Mergers in 3d Numerical Relativity

The standard approach to the numerical evolution of black hole data using the ADM formulation with maximal slicing and vanishing shift is extended to non-symmetric black hole data containing black holes with linear momentum and spin by using a time-independent conformal rescaling based on the puncture representation of the black holes. We give an example for a concrete three dimensional numerical implementation. The main result of the simulations is that this approach allows for the first time to evolve through a brief period of the merger phase of the black hole inspiral.Comment: 8 pages, 9 figures, REVTeX; expanded discussion, results unchange

Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule--width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate finite differencing, while those in the y \neq 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.Comment: 17 pages, 4 figure

Self-advancing step-tap tool

Methods and tool for simultaneously forming a bore in a work piece and forming a series of threads in said bore. In an embodiment, the tool has a predetermined axial length, a proximal end, and a distal end, said tool comprising: a shank located at said proximal end; a pilot drill portion located at said distal end; and a mill portion intermediately disposed between said shank and said pilot drill portion. The mill portion is comprised of at least two drill-tap sections of predetermined axial lengths and at least one transition section of predetermined axial length, wherein each of said at least one transition section is sandwiched between a distinct set of two of said at least two drill-tap sections. The at least two drill-tap sections are formed of one or more drill-tap cutting teeth spirally increasing along said at least two drill-tap sections, wherein said tool is self-advanced in said work piece along said formed threads, and wherein said tool simultaneously forms said bore and said series of threads along a substantially similar longitudinal axis

Inhibition of fatty acid oxidation as a therapy for MYC-overexpressing triple-negative breast cancer.

Expression of the oncogenic transcription factor MYC is disproportionately elevated in triple-negative breast cancer (TNBC), as compared to estrogen receptor-, progesterone receptor- or human epidermal growth factor 2 receptor-positive (RP) breast cancer. We and others have shown that MYC alters metabolism during tumorigenesis. However, the role of MYC in TNBC metabolism remains mostly unexplored. We hypothesized that MYC-dependent metabolic dysregulation is essential for the growth of MYC-overexpressing TNBC cells and may identify new therapeutic targets for this clinically challenging subset of breast cancer. Using a targeted metabolomics approach, we identified fatty acid oxidation (FAO) intermediates as being dramatically upregulated in a MYC-driven model of TNBC. We also identified a lipid metabolism gene signature in patients with TNBC that were identified from The Cancer Genome Atlas database and from multiple other clinical data sets, implicating FAO as a dysregulated pathway that is critical for TNBC cell metabolism. We found that pharmacologic inhibition of FAO catastrophically decreased energy metabolism in MYC-overexpressing TNBC cells and blocked tumor growth in a MYC-driven transgenic TNBC model and in a MYC-overexpressing TNBC patient-derived xenograft. These findings demonstrate that MYC-overexpressing TNBC shows an increased bioenergetic reliance on FAO and identify the inhibition of FAO as a potential therapeutic strategy for this subset of breast cancer

Self-Advancing Step-Tap Drills

Self-advancing tool bits that are hybrids of drills and stepped taps make it possible to form threaded holes wider than about 1/2 in. (about 13 mm) without applying any more axial force than is necessary for forming narrower pilot holes. These self-advancing stepped-tap drills were invented for use by space-suited astronauts performing repairs on reinforced carbon/carbon space-shuttle leading edges during space walks, in which the ability to apply axial drilling forces is severely limited. Self-advancing stepped-tap drills could also be used on Earth for making wide holes without applying large axial forces. A self-advancing stepped-tap drill (see figure) includes several sections having progressively larger diameters, typically in increments between 0.030 and 0.060 in. (between about 0.8 and about 1.5 mm). The tip section, which is the narrowest, is a pilot drill bit that typically has a diameter between 1/8 and 3/16 in. (between about 3.2 and about 4.8 mm). The length of the pilot-drill section is chosen, according to the thickness of the object to be drilled and tapped, so that the pilot hole is completed before engagement of the first tap section. Provided that the cutting-edge geometry of the drill bit is optimized for the material to be drilled, only a relatively small axial force [typically of the order of a few pounds (of the order of 10 newtons)] must be applied during drilling of the pilot hole. Once the first tap section engages the pilot hole, it is no longer necessary for the drill operator to apply axial force: the thread engagement between the tap and the workpiece provides the axial force to advance the tool bit. Like the pilot-drill section, each tap section must be long enough to complete its hole before engagement of the next, slightly wider tap section. The precise values of the increments in diameter, the thread pitch, the rake angle of the tap cutting edge, and other geometric parameters of the tap sections must be chosen, in consideration of the workpiece material and thickness, to prevent stripping of threads during the drilling/tapping operation. A stop-lip or shoulder at the shank end of the widest tap section prevents further passage of the tool bit through the hole

Three Dimensional Distorted Black Holes

We present three-dimensional, {\it non-axisymmetric} distorted black hole initial data which generalizes the axisymmetric, distorted, non-rotating [Bernstein93a] and rotating [Brandt94a] single black hole data developed by Bernstein, Brandt, and Seidel. These initial data should be useful for studying the dynamics of fully 3D, distorted black holes, such as those created by the spiraling coalescence of two black holes. We describe the mathematical construction of several families of such data sets, and show how to construct numerical solutions. We survey quantities associated with the numerically constructed solutions, such as ADM masses, apparent horizons, measurements of the horizon distortion, and the maximum possible radiation loss ($MRL$).Comment: 23 pages, 12 figures, accepted for publication in Classical and Quantum Gravit

Evolution of 3D Boson Stars with Waveform Extraction

Numerical results from a study of boson stars under nonspherical perturbations using a fully general relativistic 3D code are presented together with the analysis of emitted gravitational radiation. We have constructed a simulation code suitable for the study of scalar fields in space-times of general symmetry by bringing together components for addressing the initial value problem, the full evolution system and the detection and analysis of gravitational waves. Within a series of numerical simulations, we explicitly extract the Zerilli and Newman-Penrose scalar $\Psi_4$ gravitational waveforms when the stars are subjected to different types of perturbations. Boson star systems have rapidly decaying nonradial quasinormal modes and thus the complete gravitational waveform could be extracted for all configurations studied. The gravitational waves emitted from stable, critical, and unstable boson star configurations are analyzed and the numerically observed quasinormal mode frequencies are compared with known linear perturbation results. The superposition of the high frequency nonspherical modes on the lower frequency spherical modes was observed in the metric oscillations when perturbations with radial and nonradial components were applied. The collapse of unstable boson stars to black holes was simulated. The apparent horizons were observed to be slightly nonspherical when initially detected and became spherical as the system evolved. The application of nonradial perturbations proportional to spherical harmonics is observed not to affect the collapse time. An unstable star subjected to a large perturbation was observed to migrate to a stable configuration.Comment: 26 pages, 12 figure