Bulletin of the American Physical Society
2006 APS April Meeting
Saturday–Tuesday, April 22–25, 2006; Dallas, TX
Session I11: Focus Session: Initial Data Sets for Numerical Relativity |
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Sponsoring Units: GGR Chair: Larry Kidder, Cornell University Room: Hyatt Regency Dallas Cumberland E |
Sunday, April 23, 2006 10:30AM - 11:06AM |
I11.00001: Status of Initial Data for Binary Black Hole Collisions Invited Speaker: The first initial data for black-hole binaries were derived from analytic time-symmetric multi-hole solutions of Misner and Lindquist in the early 1960s. These served as a test-bed for all of the pioneering efforts to evolve black-hole binaries to collision. The first major revolution in this field was introduced by Bowen and York in 1980, allowed for time-asymmetric data representing boosted and spinning holes, and required the numerical solution of a single scalar boundary-value problem. Initial-data methods based on the Bowen-York extrinsic curvature were developed and explored over the last 25 years and initial data based on these methods are still widely used for black-hole binary evolutions. However, in the past 5 years, a second major revolution has taken place that promises to yield initial data that is much more astrophysically realistic. These new initial-data sets are more computationally expensive to construct and their full physical content is still being explored. In this talk, we will look at this new method for constructing black-hole binary initial data, see what it does well, and where it needs further improvement. [Preview Abstract] |
Sunday, April 23, 2006 11:06AM - 11:18AM |
I11.00002: Progress in Post-Newtonian Data for Numerical Relativity Bernard Kelly, Manuela Campanelli, Bernard Whiting, Wolfgang Tichy Physically realistic initial data for the black-hole-binary problem is expected to accord with predictions from post-Newtonian theory at sufficiently large separations. Schemes for using this idea in obtaining 3+1 initial data for black-hole binaries have recently been proposed by Tichy et al and by Nissanke. However in numerical applications based on post-Newtonian results, some difficulties have been encountered in the far-field region. We report on progress in extending these schemes up to 2.5 pN order to obtain globally well-behaved data sets that reduce asymptotically to the Kerr solution. [Preview Abstract] |
Sunday, April 23, 2006 11:18AM - 11:30AM |
I11.00003: Perfecting the Frankenstein Approach: Improved asymptotically matched initial data for non-spinning black hole binaries Nicolas Yunes, Wolfgang Tichy The accuracy of gravitational wave templates produced by numerical simulations is partially determined by the initial data chosen. A promising method to construct accurate data employs asymptotic matching to construct an approximate global 4-metric. In this talk, we will apply this method to a binary system of non-spinning black holes and discuss improvements. A global metric can be constructed by asymptotically matching two tidally perturbed Schwarzschild metrics in isotropic coordinates valid near each hole to an ADMTT post-Newtonian metric valid far from them. As a result, adjacent metrics agree in the matching region up to uncontrolled remainders in the approximations. We build a smooth global 4-metric with transition functions, carefully constructed to avoid introducing errors larger than those in the approximations. The main improvement arises by using metrics in similar coordinates before performing the matching. This similarity leads to adjacent metrics that are similar even near the horizons, thus allowing for a smoother transition and constraint violations. We also construct a map that takes this metric to Kerr-Schild coordinates near each hole. [Preview Abstract] |
Sunday, April 23, 2006 11:30AM - 11:42AM |
I11.00004: Well-posed 3+1 representation of the Bondi-Sachs problem Simonetta Frittelli Conventionally, in the case of the Einstein equations, characteristic problems have been stated in the Bondi-Sachs form, whereas Cauchy-problems have been formulated in the ADM form, and both problems have been pursued independently of each other. Yet characteristic and Cauchy problems are only two sides of the same differential equations. Under the restriction of spherical symmetry, we provide a 3+1 version of the Einstein equations that functions as the initial-value representation of the Bondi-Sachs equations. This is a well-posed ADM formulation that allows us to interpret the Bondi-Sachs variables precisely in terms of outgoing characteristic fields. The ADM form is automatically first-order in time, with no need for reduction. Both these features have relevance to numerical simulations. We indicate which of the features are maintained when the assumption of symmetry is removed. [Preview Abstract] |
Sunday, April 23, 2006 11:42AM - 11:54AM |
I11.00005: Spin Dependence in Computational Black-Hole Data Scott Hawley, Richard Matzner, Michael Vitalo We have implemented an parallel multigrid solver, to solve the initial data problem for $3+1$ General Relativity. This involves solution of elliptic equations derived from the Hamiltonian and the momentum constraints. We use the conformal transverse-traceless method of York and collaborators, which consists of a conformal decomposition with a scalar $\phi$ that adjusts the metric, and a vector potential $w^i$ that adjusts the longitudinal components of the extrinsic curvature. The constraint equations are then solved for these quantities $\phi$, $w^i$ such that the complete solution fully satisfies the constraints. We apply this technique to confirm theoretical expectations for the spin -orientation and -separation dependence in the case of spinning interacting black holes, and we investigate some of the nonlinear effects in initial data for binary black hole interactions. [Preview Abstract] |
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