Bulletin of the American Physical Society
2005 APS April Meeting
Saturday–Tuesday, April 16–19, 2005; Tampa, FL
Session J10: Numerical Relativity I |
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Sponsoring Units: GGR Chair: Beverly Berger, National Science Foundation Room: Marriott Tampa Waterside Room 6 |
Sunday, April 17, 2005 10:45AM - 10:57AM |
J10.00001: Towards Wave Extraction in Numerical Relativity: Transverse Frames Christopher Beetle, Lior Burko This presentation will discuss new developments in a theoretical program to extract the gravitational wave content of a space- time containing a quiescent black hole. The central idea of this program is to seek invariant quantities which may be defined using only the physical metric on space-time, without reference to perturbation expansions or similar background structures, yet which at least partially characterize gravitational radiation fields in those cases where such radiation is incontrovertibly present. This work is expected to be relevant to numerical relativity since it should be possible, at least in principle, to apply its techniques to numerical space-times describing such quiescent black holes. These space- times could describe, for example, the late stages of collisions of binary systems or of supernovae. The goal here, then, is to recover from the late-time numerical data some genuinely gauge- invariant information concerning the radiation generated strongly dynamical processes at earlier times. [Preview Abstract] |
Sunday, April 17, 2005 10:57AM - 11:09AM |
J10.00002: Towards Wave Extraction in Numerical Relativity: Analytical Examples Lior Burko, Thomas Baumgarte, Christopher Beetle Beetle and Burko recently introduced a scalar curvature invariant for general relativity, that carries information about gravitational radiation in generic spacetimes, in cases where such radiation is incontrovertibly defined. Here, we find the Beetle-Burko scalar explicitly for a number of analytical examples (including Bowen-York initial data and linearized quadrupole waves). We discuss the insights into numerical relativity wave extraction that may be learned from these examples, in addition to analytical and scaling properties of the Beetle-Burko scalar. We argue that the Beetle-Burko scalar is an invaluable tool for wave extraction in numerical relativity, in addition to a means for estimating the wave content of initial data sets. [Preview Abstract] |
Sunday, April 17, 2005 11:09AM - 11:21AM |
J10.00003: LazarusII: Applying the Quasi-Kinnersley Frame to Numerical Evolutions Bernard Kelly, Carlos Lousto, Manuela Campanelli The Lazarus project was designed to make the most of limited 3D black-hole simulations, through the identification of radiation at late times, and subsequent evolution of the Weyl scalar $\Psi_4$ through the Teukolsky formulation. We report on new developments in Lazarus, employing the concept of the ``quasi-Kinnersley'' frame to analyze late-time numerical space-times that we suspect differ only slightly from Kerr. This allows us to extract unambiguous information about the ``background'' Kerr solution, and through this, to identify the radiation present. These techniques will enable us to validate previous Lazarus results, and to resolve some, if not all, of the coordinate uncertainties encountered in interpreting the results of black-hole simulations. [Preview Abstract] |
Sunday, April 17, 2005 11:21AM - 11:33AM |
J10.00004: Binary black hole wave extraction - results with Mesh Refinement Breno Imbiriba, John Baker We apply numerical simulations with mesh refinement in a Lazarus-type model for radiation from a binary black hole system. This technique begins with a full 3D, nonlinear, evolution of a binary black hole system. We apply mesh refinement to enable high resolution finite differencing at the punctures while placing the outer boundary sufficiently far. This evolution is carried out using the BSSN equations and the ``1+log'' gauge. Data from the final stages of that evolution are used to construct initial data for the Teukolsky perturbation equation, which continues the evolution, treated as curvature perturbations of a Kerr black hole. [Preview Abstract] |
Sunday, April 17, 2005 11:33AM - 11:45AM |
J10.00005: Propagating gravitational waves through mesh refinement boundaries David Fiske, John Baker, Joan Centrella We explore the numerical propagation of gravitational waves across mesh refinement boundaries. We define these waves via the Weyl scalars in the Newman-Penrose formalism, and evolve a linearized wave solution with a non-linear Einstein evolution code. Because we have an analytic solution for the spacetime modeled, we are able to verify that the waves do propagate faithfully through mesh refinement boundaries, paving the way for future work in which strong-field sources generate waves that we would like to track across refinement regions. Looking forward to applications in which we would like to extract spherical harmonic components of waves, we also apply, for the first time, a novel method for computing spherical harmonic components of data represented on a cubic grid. We show that, even though the integration spheres intersect refinement boundaries, it produces accurate and robust results. [Preview Abstract] |
Sunday, April 17, 2005 11:45AM - 11:57AM |
J10.00006: Conformal thin-sandwich puncture initial data for boosted black holes Mark Hannam, Greg Cook We have applied the puncture approach to conformal thin-sandwich black-hole initial data. I will present a procedure to numerically construct conformal thin-sandwich puncture (CTSP) initial data for multiple black holes, each with non-zero linear momentum, and present results for single boosted-black-hole initial-data sets. Conformally flat solutions for a boosted black hole are found to have the same maximum gravitational radiation content as the corresponding Bowen-York solution in the conformal transverse-traceless decomposition. [Preview Abstract] |
Sunday, April 17, 2005 11:57AM - 12:09PM |
J10.00007: Radiated Net Angular Momentum from Numerical Evolution of Black Hole Spacetimes ryoji Takahashi We examine the conservation of net angular momentum from numerical evolution of single rotation black hole spactimes. From full 3D numerical evolution, we show that there is no net angular momentum radiate from axisymmetric data. We also show that net angular momentum radiated in gravitational waves consistent with measurements from horizon oscillations from non-axisymmetric data. From those results may address the question to current mathematical construction of binary black initial data of inner stable circular orbit. [Preview Abstract] |
Sunday, April 17, 2005 12:09PM - 12:21PM |
J10.00008: Understanding the fate of merging supermassive black holes Carlos Lousto, Manuela Campanelli Understanding the fate of merging supermassive black holes in galactic mergers, and the gravitational wave emission from this process, are important LISA science goals. To this end, we present results from numerical relativity simulations of binary black hole mergers using the so-called Lazarus approach to model gravitational radiation from these events. In particular, we focus here on some recent calculations of the final spin and recoil velocity of the remnant hole formed at the end of a binary black hole merger process, which may constraint the growth history of massive black holes at the core of galaxies and globular clusters. [Preview Abstract] |
Sunday, April 17, 2005 12:21PM - 12:33PM |
J10.00009: Finite Elements in Numerical Relativity Matthew Anderson We employ finite elements in solving the Einstein equations for black hole spacetimes. Numerical simulation of black hole spacetimes requires special treatment for the singularity inside a black hole. One common approach is to excise the singularity from the computational domain. Recent analysis has emphasized the importance of using smooth excision regions to achieve stable black hole evolutions. Smooth excision regions can be produced easily using unstructured meshes. Solving the Einstein equations requires solving equations of two types: the elliptic initial data ( constraint ) equations and evolution equations. We present examples of solving both types of equations for both black hole and black string spacetimes using the finite element method. [Preview Abstract] |
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