Bulletin of the American Physical Society
APS April Meeting 2014
Volume 59, Number 5
Saturday–Tuesday, April 5–8, 2014; Savannah, Georgia
Session J15: Numerical Relativity in Vacuum: Methods and Simulation I |
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Chair: Francois Foucart, University of Toronto Room: 103 |
Sunday, April 6, 2014 10:45AM - 10:57AM |
J15.00001: Local Geometrical Boundary Data for Einstein's Equations Jeffrey Winicour An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic curvature of the initial Cauchy hypersurface, subject to constraints. This Cauchy data determine a solution to Einstein's equations which is unique up to a diffeomorphism. In joint work with H.-O. Kreiss, we show how three pieces of unconstrained boundary data, which are associated locally with the geometry of the boundary, likewise determine a solution of the initial-boundary value problem which is unique up to a diffeomorphism. One piece of this data, constructed from the extrinsic curvature of the boundary, determines the dynamical evolution of the boundary. The other two pieces constitute a conformal class of rank-2 metrics, which represent the two gravitational degrees of freedom. [Preview Abstract] |
Sunday, April 6, 2014 10:57AM - 11:09AM |
J15.00002: Spectral Cauchy Characteristic Extraction: A New Algorithm for Gravitational Wave Propagation Casey Handmer, B\'ela Szil\'agyi We present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral Cauchy Characteristic Extraction (CCE), a thorough method for obtaining valid gravitational waveforms from existing and future astrophysical simulations. We demonstrate the new algorithm's stability, convergence, and agreement with existing CCE methods. We explain how an innovative spectral approach enables greatly improved computational efficiency. [Preview Abstract] |
Sunday, April 6, 2014 11:09AM - 11:21AM |
J15.00003: Adding light to the gravitational waves on the null cone Maria Babiuc Recent interesting astrophysical observations point towards a multi-messenger, multi-wavelength approach to understanding strong gravitational sources, like compact stars or black hole collisions, supernovae explosions, or even the big bang. Gravitational radiation is properly defined only at future null infinity, but usually is estimated at a finite radius, and then extrapolated. Our group developed a characteristic waveform extraction tool, implemented in an open source code, which computes the gravitational waves infinitely far from their source, in terms of compactified null cones, by numerically solving Einstein equation in Bondi space-time coordinates. The goal is extend the capabilities of the code, by solving Einstein-Maxwell's equations together with the Maxwell's equations, to obtain the energy radiated asymptotically at infinity, both in gravitational and electromagnetic waves. The purpose is to analytically derive and numerically calculate both the gravitational waves and the electromagnetic counterparts at infinity, in this characteristic framework. The method is to treat the source of gravitational and electromagnetic radiation as a black box, and therefore the code will be very flexible, with potentially large applicability. [Preview Abstract] |
Sunday, April 6, 2014 11:21AM - 11:33AM |
J15.00004: Improved Gauge Conditions and Evolution Techniques for Puncture Black Hole Simulations Zachariah Etienne, John Baker, Vasileios Paschalidis, Stuart Shapiro, Bernard Kelly Robust spacetime gauge conditions are critically important to the stability and accuracy of numerical relativity (NR) simulations involving puncture black holes. Most of the NR community continues to use the highly-robust---though nearly decade-old---``moving-puncture gauge conditions'' for such simulations. We present improved gauge conditions and evolution techniques that reduce constraint violations by more than an order of magnitude on adaptive-mesh refinement (AMR) grids. It has been found that high-frequency waves propagating away from puncture black holes (e.g., in binary systems) cross progressively lower levels of refinement until they become under-resolved and reflect off an AMR boundary, leading to noisy gravitational waveforms. Such noise does not converge away cleanly with increasing resolution, effectively setting a hard upper limit on waveform accuracy using puncture techniques at computationally feasible resolutions. We demonstrate that our improved puncture gauge conditions reduce this noise by nearly an order of magnitude, and point to possible directions for future improvements. [Preview Abstract] |
Sunday, April 6, 2014 11:33AM - 11:45AM |
J15.00005: Improved initial data for binary black hole simulations William Throwe Asymptotically matched approximate analytic metrics can provide realistic initial data for binary black hole simulations. We have simulated these data using the Spectral Einstein Code (SpEC) and observe that they show decreased junk radiation and physical parameter drift as compared to commonly used initial data. We have generalized previous asymptotically matched data sets to allow for arbitrary initial hole velocities, and have demonstrated that this method can be used to adjust the eccentricity of the simulated binaries, including describing binary systems with quasicircular orbits. [Preview Abstract] |
Sunday, April 6, 2014 11:45AM - 11:57AM |
J15.00006: Detecting Near-Extremal Binary Black Holes Daniel Hemberger There is an ongoing effort in the gravitational wave astronomy community to construct a template bank for Advanced LIGO that includes gravitational waveforms from binary black hole systems with high mass ratios and spins. Using numerical relativity simulations performed with the Spectral Einstein Code, we assess the prospects for detection and parameter estimation of binaries with spins above the expected template bank cutoff spin. This analysis is restricted to equal-mass, non-precessing binaries. [Preview Abstract] |
Sunday, April 6, 2014 11:57AM - 12:09PM |
J15.00007: Simulations of high-spin black-hole binaries Mark Scheel, Geoffrey Lovelace Black holes can in principle have spins up to the Kerr limit $a=1$, and some (highly uncertain) estimates from X-ray binaries yield $a>0.98$. Because binaries with highly-spinning black holes may be detectable by LIGO, it is important to be able to simulate and understand these systems. We present binary black hole simulations with large spins, including a generic, precessing simulation with a spin of $a>0.99$ on one of the black holes. We discuss some of the difficulties with simulating high-spin black holes and how to overcome them. [Preview Abstract] |
Sunday, April 6, 2014 12:09PM - 12:21PM |
J15.00008: Numerical Relativity reaching into the land of Post-NewtonianTheory Bela Szilagyi Extensive code improvement of the Spectral Einstein Code has made it now possible for us to perform simulations that start at frequencies where Post Newtonian Theory is accurate. As a first such run we have performed a 175 orbit, mass-ratio 7, non-spinning BBH run at several resolutions. Runs of this type open the gate towards a new level of testing of the various BBH waveform approximants. The important question of ``how long should runs be'' receives a new meaning. The talk will focus on current status as well as future plans for these ultra-long simulations. [Preview Abstract] |
Sunday, April 6, 2014 12:21PM - 12:33PM |
J15.00009: Comparing Post-Newtonian and Numerical Relativity Precession Dynamics Serguei Ossokine, Michael Boyle, Lawrence Kidder, Abdul Mroue, Harald Pfeiffer, Mark Scheel, Bela Szilagyi Binary compact objects are expected to be some of the best sources for gravitational wave signals for the second generation gravitational wave detectors such as Advanced LIGO and Virgo. Post-Newtonian theory is one of the leading ways of approximately modeling such systems, however it is expected to be inaccurate in the strong-field regime, which has been quantified for non-precessing systems by many groups. In this talk, a systematic comparison of numerical relativity simulations of precessing binary black holes from the SpEC public catalog to Post-Newtonian approximants is discussed. The focus of the work is on the orbital dynamics of the system -- in particular, the precession of the orbital plane and the black hole spins, as well as the orbital phasing. [Preview Abstract] |
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