Bulletin of the American Physical Society
APS April Meeting 2012
Volume 57, Number 3
Saturday–Tuesday, March 31–April 3 2012; Atlanta, Georgia
Session W8: Topics in Numerical Relativity |
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Sponsoring Units: GGR Chair: Manuel Tiglio, University of Maryland College Park Room: Embassy B |
Tuesday, April 3, 2012 10:45AM - 10:57AM |
W8.00001: The Einstein Toolkit Frank L\"{o}ffler The Einstein Toolkit Consortium is developing and supporting open software for relativistic astrophysics. Its aim is to provide the core computational tools that can enable new science, broaden our community, facilitate interdisciplinary research and take advantage of petascale computers and advanced cyberinfrastructure. The Einstein Toolkit currently consists of an open set of over 100 modules for the Cactus framework, primarily for computational relativity along with associated tools for simulation management and visualization. The toolkit includes solvers for vacuum spacetimes as well as relativistic magneto-hydrodynamics, along with modules for initial data, analysis and computational infrastructure. These modules have been developed and improved over many years by many different researchers. The Einstein Toolkit is supported by a distributed model, combining core support of software, tools, and documentation in its own repositories and through partnerships with other developers who contribute open software and coordinate together on development. As of January 2012 it has 68 registered members from 30 research groups world-wide. This talk will present the current capabilities of the Einstein Toolkit and will point to information how to leverage it for future research. [Preview Abstract] |
Tuesday, April 3, 2012 10:57AM - 11:09AM |
W8.00002: Continuum and discrete initial-boundary value problems and the Einstein field equations Manuel Tiglio, Olivier Sarbach In this talk we outline some of the theory necessary to understand continuum and discrete initial-boundary value problems arising from hyperbolic partial differential equations, and discuss applications to numerical relativity. In particular, we present a well posed initial and initial-boundary value formulations for Einstein's equations, and discuss multi-domain high order finite difference techniques and spectral methods to discretize them. The talk is a very brief outline of the contents of an upcoming Living Review in Relativity, ``Continuum and discrete initial boundary value problems and the Einstein field equations,'' by Olivier Sarbach and Manuel Tiglio. [Preview Abstract] |
Tuesday, April 3, 2012 11:09AM - 11:21AM |
W8.00003: A conformal thin-sandwich solver for generic initial data Fethi M. Ramazanoglu, William E. East, Frans Pretorius We will present our recently implemented code for an initial data (ID) solver for general relativity, IDSolve. A 3+1 decomposition breaks the Einstein Equations into two groups: hyperbolic ``evolution equations'' and elliptic ``constraint equations.'' IDSolve aims to provide physically meaningful data that satisfies the constraint equations, which can be used as initial data in numerical evolution. IDSolve uses the Conformal Thin Sandwich (CTS) method and does not assume any symmetries or simplifications of the equations of CTS, unlike most of the currently used ID solvers. Specifically, it does not assume the freely specified conformal spatial metric to be flat. IDSolve uses a parallelized multi-grid (MG) elliptic solver with adaptive mesh refinement (AMR) to solve the CTS equations. Singularities are avoided using a regularization scheme. I will present our results of binary object initial data, for which the generality of our code enables us to set the CTS free data using a superposition of the exactly known single object space-times. [Preview Abstract] |
Tuesday, April 3, 2012 11:21AM - 11:33AM |
W8.00004: Numerical simulations with a First order BSSN formulation of Einstein's field equations David Brown, Peter Diener, Scott Field, Jan Hesthaven, Frank Herrmann, Abdul Mroue, Olivier Sarbach, Erik Schnetter, Manuel Tiglio, Michael Wagman We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. In particular, we describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement and in particular binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. These results constitute a first step in an effort to combine the robustness of BSSN evolutions with very high accuracy numerical techniques, such as spectral collocation multi-domain or discontinuous Galerkin methods. [Preview Abstract] |
Tuesday, April 3, 2012 11:33AM - 11:45AM |
W8.00005: Resolving Topological Features of Black Hole Event Horizons Jeff Kaplan, Michael Cohen, Mark Scheel We examine the structure of the event horizon for numerical simulations of two black holes that begin in a quasicircular orbit, inspiral, and finally merge. We find that the spatial cross section of the merged event horizon has spherical topology (to the limit of our resolution), despite the expectation that generic binary black hole mergers in the absence of symmetries should result in an event horizon that briefly has a toroidal cross section. We investigate how the choice of time slicing affects both the spatial cross section of the event horizon and the locus of points at which generators of the event horizon cross. Building on previous work and using the intuition gained from our numerical results, we deduce the precise mathematical condition necessary for the existence of a toroidal horizon in a given spatial slice. Since we seek to make claims about topological features of the event horizon, we ensure the robustness of our conclusions by checking our results at multiple numerical resolutions. We find that the structure of the horizon generators in our simulations is consistent with expectations, and the lack of toroidal horizons in our simulations is due to our choice of time slicing. [Preview Abstract] |
Tuesday, April 3, 2012 11:45AM - 11:57AM |
W8.00006: Using Radial Basis Functions to Interpolate along Single-Null Characteristics Maria Babiuc, Clyde-Emmanuel Meador The Cauchy-Characteristic Extraction (CCE) technique is the most precise method available for the computation of the gravitational waves obtained from numerical simulations of binary black hole mergers. This technique utilizes the characteristic evolution to extend the simulation to null infinity, where the waveform is computed in inertial coordinates. Although we recently made CCE publicly available to the numerical relativity community, there is still room for improvement, and the most important is enhancing the overall accuracy of the code, by upgrading the numerical methods used for interpolation and differentiation. One of the most promising ways is to use the Radial Basis Functions (RBFs) method, which is grid independent, and provides spectrally accurate solutions. We used the multiquadric RBFs to do the interpolation and differentiation on the characteristic. Our tests indicate that the RBFs method gives significantly better results for a single-null characteristic than the finite-difference methods used currently in the code. This is a work in progress toward improving the accuracy of the code, which is relevant for the new generation of advanced gravitational wave detectors. [Preview Abstract] |
Tuesday, April 3, 2012 11:57AM - 12:09PM |
W8.00007: Binary Black Holes: Are the Scalar-Tensor and General Relativistic Versions Indistinguishable? Clifford Will It is known from a theorem of Hawking that asymptotically flat, stationary black holes in Brans-Dicke theory are identical to those in general relativity, because any scalar ``hair'' is radiated away, leaving a spatially constant field that leaves the geometry indistinguishable from general relativity. What about binary black holes in generic Scalar-Tensor (ST) theories? We argue that recent work analyzing ST black holes in a background cosmology, ST binary black holes in post-Newtonian theory and perturbation theory, and ST black hole mergers using numerical relativity suggest that vacuum, asymptotically flat binary black holes in ST theories without a scalar field potential may be observationally indistinguishable from their counterparts in general relativity. [Preview Abstract] |
Tuesday, April 3, 2012 12:09PM - 12:21PM |
W8.00008: Late Inspiral and Merger of Binary Black Holes in Scalar-Tensor Theories of Gravity James Healy, Tanja Bode, Roland Haas, Enrique Pazos, Pablo Laguna, Deirdre Shoemaker, Nicolas Yunes Gravitational wave observations will probe non-linear gravitational interactions and thus enable strong tests of Einstein's theory of general relativity. We present a numerical relativity study of the late inspiral and merger of binary black holes in scalar-tensor theories of gravity. We consider black hole binaries in an inhomogeneous scalar field, specifically binaries inside a scalar field bubble, in some cases with a potential. We calculate the emission of dipole radiation. We also show how these configurations trigger detectable differences between gravitational waves in scalar-tensor gravity and the corresponding waves in general relativity. We conclude that, barring an external mechanism to induce dynamics in the scalar field, scalar-tensor gravity binary black holes alone are not capable of awaking a dormant scalar field, and are thus observationally indistinguishable from their general relativistic counterparts. [Preview Abstract] |
Tuesday, April 3, 2012 12:21PM - 12:33PM |
W8.00009: Numerical Simulations of Domain Wall Collapse David Garfinkle Numerical simulations are performed of the gravitational collapse of several types of thick domain walls. In each case, the properties of the resulting black holes are found. [Preview Abstract] |
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