Bulletin of the American Physical Society
2005 APS April Meeting
Saturday–Tuesday, April 16–19, 2005; Tampa, FL
Session M10: Numerical Relativity II |
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Sponsoring Units: GGR Chair: Chris Beetle, Florida Atlantic University Room: Marriott Tampa Waterside Room 6 |
Sunday, April 17, 2005 3:15PM - 3:27PM |
M10.00001: Testing Formulations with Binary Neutron Star Simulations Pedro Marronetti New formulations for the evolution of gravitational fields in numerical relativity are continuously presented to the scientific community. Their main goal is to achieve stable and reliable evolutions of compact-object binaries. However, due to the complexity of the required numerical work, few of the many formulations found in the literature have been tested on binary evolutions. We introduce in this paper a new testing ground for numerical methods based on the simulation of binary neutron stars (BNS). Our objective is to benchmark new formalisms against the currently most stable simulations. BNS simulations usually require extensive computational resources and the length of the runs could, in principle, render these tests impractical. Here we show how small, low resolution grids can be used to gain insight into the stability of different numerical schemes, with runs that only take a few hours on single-processor workstations. [Preview Abstract] |
Sunday, April 17, 2005 3:27PM - 3:39PM |
M10.00002: General Relativistic Hydrodynamics with Viscosity Matthew D. Duez, Yuk Tung Liu, Stuart L. Shapiro, Branson C. Stephens Viscosity and magnetic fields drive differentially rotating stars toward uniform rotation, and this process has important consequences in many astrophysical contexts. Here, we present the first numerical evolutions of rapidly rotating stars with shear viscosity in full general relativity. We self-consistently include viscosity in our relativistic hydrodynamic code by solving the fully relativistic Navier-Stokes equations in a BSSN formulation. We demonstrate the ability of our code to accurately follow both the {\it secular} viscous evolution of differentially rotating stars for many rotation periods, as well as dynamical evolution. We also investigate the ability of viscosity to drive bar or disk formation. [Preview Abstract] |
Sunday, April 17, 2005 3:39PM - 3:51PM |
M10.00003: Viscous Evolution of Hypermassive Neutron Stars in Full General Relativity Matthew Duez, Yuk Tung Liu, Stuart Shapiro, Branson Stephens Hypermassive neutron stars may form from merging binary neutron stars or stellar core collapse. While they are dynamically stable due to extra centrifugal support from differential rotation, their structure changes on a secular timescale when magnetic fields and/or viscosity gradually remove the differential rotation support. We evolve these stars with viscosity using a fully general relativitic hydrodynamics code based on the BSSN formulation of Einstein's equations. We find that viscosity operating in a hypermassive star generically leads to the formation of a compact, uniformly rotating core surrounded by a low-density disk. These uniformly rotating cores are often, but not always, unstable to gravitational collapse. We follow the collapse in such cases and, using black hole excision, determine the mass and the spin of the final black hole and ambient disk. In all cases studied, the rest mass of the resulting disk is found to be 10-20\% of the original star, whether surrounding a uniformly rotating core or a rotating black hole. [Preview Abstract] |
Sunday, April 17, 2005 3:51PM - 4:03PM |
M10.00004: Evolution of 3D Boson Stars with Waveform Extraction Ruxandra Bondarescu, Jayashree Balakrishna, Gregory Daues, Francisco Guzman, Edward Seidel This talk will present results from a study of boson stars under nonspherical perturbations using a fully general-relativistic 3D code based on the Cactus Computational Toolkit. We study the evolution of stable, critical and unstable boson stars subjected to various types of nonspherical perturbations and analyze the emitted gravitational waves. We calculate the Zerilli and Newman-Penrose $\Psi_4$ gravitational waveforms and study the quasinormal mode content of the numerical waveforms using predicted QNM frequencies from perturbation theory calculations of Yoshida, Eriguchi and Futamase. Our results show that the waveforms accurately display the strong damping predicted for quasinormal modes of boson stars. The apparent horizons formed from perturbed unstable star collapse were observed to be slightly nonspherical when initially detected and became more spherical as the system evolved. [Preview Abstract] |
Sunday, April 17, 2005 4:03PM - 4:15PM |
M10.00005: Introducing the LazEv Evolution Code for 3+1 Gravity Yosef Zlochower, John Baker, Manuela Campanelli, Carlos Lousto We have developed a generalized code to solve the Cauchy Initial Value Problem (with boundaries) for the Einstein Equations using a variety of 3+1 decompositions. The time integration is carried out using the `Method of Lines' with ICN and Runge Kutta style integrators (up to fourth-order), and the spatial derivatives are evaluated using a variety of finite differencing operators (both centered and upwinded) with up to sixth-order accuracy. We have currently implemented the ADM formulation as well as several `flavors' of the BSSN formulation, and used the code to evolve puncture data for single distorted black-holes, head-on collisions of binary black holes, and orbiting binary black-holes. We also tested the code by evolving the linear wave, gauge wave, and Gowdy wave testbeds. Here we describe the features of this code and show convergence plots and waveforms. We also describe some technical difficulties encountered when evolving puncture data with fourth-order techniques. We conclude by demonstrating that fourth-order BSSN evolutions give significantly improved Lazarus waveforms over second-order BSSN and fourth-order ADM evolutions. [Preview Abstract] |
Sunday, April 17, 2005 4:15PM - 4:27PM |
M10.00006: Consistent discretization of the Gowdy cosmologies Jorge Pullin We report joint work with Rodolfo Gambini and Marcelo Ponce in which the consistent discretization scheme (a way of discretizing constrained theories in such a way that the constraints are satisfied, with potentially interesting applications in quantum gravity as well) to the Gowdy cosmologies. This is the first time the formalism is applied to a situation with field-theoretic degrees of freedom. The numerics is quite challenging since the resulting equations are implicit and coupled. We show successful and convergent evolutions for the ``gauge wave'' situation. [Preview Abstract] |
Sunday, April 17, 2005 4:27PM - 4:39PM |
M10.00007: Scalar perturbations of higher-dimensional rotating and ultra-spinning black holes George Siopsis, Vitor Cardoso, Shijun Yoshida We investigate the stability of higher-dimensional rotating black holes against scalar perturbations. In particular, we make a thorough numerical and analytical analysis of six-dimensional black holes, not only in the low rotation regime but in the high rotation regime as well. Our results suggest that higher dimensional Kerr black holes are stable against scalar perturbations, even in the ultra-spinning regime. [Preview Abstract] |
Sunday, April 17, 2005 4:39PM - 4:51PM |
M10.00008: Energy Conditions and Junction Conditions Sho Yaida, Donald Marolf It is well known from the work of Israel that one may construct "thin shell" solutions to the Einstein Equations in which the metric induced metric along the shell is continuous across it, but for which the extrinsic curvature jumps by an amount proportional to $T_{ab}$. One might, however, ask if these are the only solutons. That is, might there be other thin shell solutions in which the induced metric is not continuous? This talk will report partial results supporting the conjecture that any additional solutions must violate the weak null energy condition. In particular, we present a theorem showing that, given any sequence of diagonal metrics which 1) satisfies the weak null energy condition and 2) converges to a thin shell spacetime, the induced geometry along the shell in the limiting spacetime is in fact continuous across it. Thus the limiting spacetime falls within the class studied by Israel. [Preview Abstract] |
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M10.00009: Approximate binary black hole initial data from matched asymptotic expansions Nicolas Yunes, Wolfgang Tichy, Benjamin Owen, Bernd Bruegmann We present astrophysically realistic approximate initial data for a binary black hole system. Near each black hole, the metric is given by the Schwarzschild solution plus a tidal perturbation due to the presence of the other black hole. Well outside each black hole, the metric is given by a post-Newtonian expansion. We use asymptotic matching together with a smooth transition function to glue the post-Newtonian and perturbed Schwarzschild solutions together. This procedure results in a smooth $C^\infty$ initial data set that is globally valid. We present explicit results for the 3-metric, extrinsic curvature, lapse, and shift. We also discuss both the errors in the physical content of these data and how well these data satisfy the constraint equations of General Relativity. [Preview Abstract] |
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