Bulletin of the American Physical Society
APS April Meeting 2010
Volume 55, Number 1
Saturday–Tuesday, February 13–16, 2010; Washington, DC
Session A14: Gravitational Collapse and Numerical Relativity |
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Sponsoring Units: GGR Chair: John Baker, NASA Goddard Space Flight Center Room: Washington 4 |
Saturday, February 13, 2010 8:30AM - 8:42AM |
A14.00001: Gravitational Waves from Core-Collapse Supernova using CHIMERA: Models and Numerical Methods Pedro Marronetti, Konstantin Yakunin, Stephen Bruenn, John Blondin, Austin Chertkow, Charlotte Dirk, William R. Hix, Eric Lentz, O.E. Bronson Messer, Anthony Mezzacappa CHIMERA is a multi-dimensional code composed of three tightly coupled physics modules: VH1 used to evolve stellar gas hydrodynamics, MGFLD-TRANS which handles the neutrino transport, and XNET that describes the thermonuclear reactions. These are complemented with a sophisticated equation of state for nuclear matter (Lattimer-Swesty) and a self-gravity solver capable of an approximation to general-relativistic gravity. We will present the latest simulations of core-collapse supernova for different-mass progenitors. These models are evolved for up to one second in all cases, making them some of longest term simulations of their kind. [Preview Abstract] |
Saturday, February 13, 2010 8:42AM - 8:54AM |
A14.00002: A new open-source spherically-symmetric general-relativistic hydrodynamics code for the study of stellar collapse and black hole formation Evan O'Connor, Christian Ott We present a new open-source general-relativistic (GR) code based on the formulation of Romero-Ibanez and employing radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction of state variables at cell interfaces and approximate Riemann solvers. The GRHD part of the code is coupled to various finite-temperature microphysical equations of state and an approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. An array of test calculations is presented. [Preview Abstract] |
Saturday, February 13, 2010 8:54AM - 9:06AM |
A14.00003: Numerical experiments testing the Kerr Limit, Naked Singularities and Surface Gravity Pablo Laguna, Tanja Bode, Richard Matzner We present results from numerical relativity simulations of accretion onto a black hole puncture. The simulations are aimed at investigating the possibility of violating the Kerr limit of rotating black holes. In particular, we focus our attention on the evolution of apparent horizons and the corresponding measure of mass, angular momentum and surface gravity. We address the challenges associated with identifying naked singularities in numerical simulations. [Preview Abstract] |
Saturday, February 13, 2010 9:06AM - 9:18AM |
A14.00004: Variational Integrators for Numerical Relativity Will Farr I present a new method for numerical simulations of general relativistic systems that eliminates constraint violating modes without the need for constraint damping. The method is a type of variational integrator. It is based on a discretization of an action for gravity (the Pleba\'{n}ski action) on an unstructured mesh that preserves the local Lorentz transformation and diffeomorphism symmetries of the continuous action. Applying Hamilton's principle of stationary action gives discrete field equations on the mesh. For each gauge degree of freedom there is a corresponding discrete constraint; the remaining discrete evolution equations exactly preserve these constraints under time-evolution. I validate the method using simulations of several analytically solvable spacetimes: a weak gravitational wave spacetime, the Schwarzschild spacetime, and the Kerr spacetime. [Preview Abstract] |
Saturday, February 13, 2010 9:18AM - 9:30AM |
A14.00005: Error Reduction in Numerical Relativity Calculations Using Local Coordinates William Darian Boggs, John G. Baker, James R. Van Meter, Joan Centrella In simulations of binary black hole systems, errors in the local calculations are determined in part by the coordinate system in which they are performed. Calculating the field quantities in coordinate systems matched to the local dynamics of each portion of the simulation grid promises to reduce this local error. I will talk about my implementation of this technique in our numerical relativity code, HAHNDOL, and its potential to improve the accuracy and efficiency of our simulations and allow us to perform more ambitious simulations. [Preview Abstract] |
Saturday, February 13, 2010 9:30AM - 9:42AM |
A14.00006: Studying competitive critical behavior in problems of gravitational collapse, using numerical relativity Theodor Brasoveanu Einstein equations, with or without coupling to matter, admit special strong-field, non-trivially dynamic solutions which sit at the threshold of black hole formation. These solutions, initially discovered by M. Choptuik, are minimally unstable and can be obtained by studying parametrized families of initial data, where the family parameter can be tuned to control the amount of non-linearity in the generated spacetime. Following the recent introduction of ``competitive critical behavior'' by the same author, we study the interaction between two different matter models in spherical symmetry that exhibit the same type of threshold solution. Specifically, we look at a a boson star vs. an SU(2) Yang-Mills perturbing field, to investigate if competitive critical behavior occurs and find out whichever solution becomes unstable in the presence of the other. We use finite-difference approximations of PDEs to solve Einstein equations coupled to matter, find the (type I) threshold of black hole formation for each individual matter system and study the relative stability of the two critical solutions. [Preview Abstract] |
Saturday, February 13, 2010 9:42AM - 9:54AM |
A14.00007: Petrov Classification in Numerical Relativity Robert Owen The algebraic classification system of Petrov, Pirani, and Penrose provides a method to unambiguously characterize the gravitational degrees of freedom point-by-point throughout a spacetime. It is tempting to apply this system to the numerically-generated spacetimes that have recently proliferated, and some work has already gone in this direction. However, spacetimes of current physical interest --- such as binary black hole mergers --- raise subtleties in that they are generically, strictly speaking, Type I, but approximately, in some sense, Type D. To make any such claims about ``approximate Petrov class'' meaningful, one must introduce a ``degeneracy measure'' on the space of null rays. In this talk, I will describe some of the difficulties in this undertaking, and present results applying such degeneracy measures to binary black hole simulations from the Caltech/Cornell/CITA group. [Preview Abstract] |
Saturday, February 13, 2010 9:54AM - 10:06AM |
A14.00008: Late time Kerr tails Gaurav Khanna, Lior M. Burko We revisit the question of the decay rate of the late time tails of Kerr black holes. We focus on three interrelated phenomena: (a) Excited ``up'' modes (i.e., the decay rate of modes of a higher multipole moment than the initial mode), (b) the apparent breakdown of linear superposition, and (c) the differences in the evolutions of pure mode initial data sets and those of generic initial data sets. Specifically, letting $\ell$ being the multipole moment of the initial data, and $\ell'$ being the moment of an excited mode (so that $\ell'>\ell$), we find for the case of scalar field perturbations that the late time decay rate behaves like $t^{-n}$, where $n=\ell+\ell'+3$. This result has been verified numerically for $\ell'-\ell=2,4$. Pure-- and generic--mode evolutions are found to be different because the former involve non-generic, specially fine--tuned evolutions. [Preview Abstract] |
Saturday, February 13, 2010 10:06AM - 10:18AM |
A14.00009: Exact Solutions to Einstein's Field Equations for Static Spherically Symmetric Perfect Fluids Thomas Kiess In classical general relativity, exact solutions to Einstein's Field Equations are useful, but for static spherically symmetric perfect fluids, only a handful of their exact closed form metrics satisfy the physical boundary conditions. We derive exact solutions to Einstein's Field Equations for a static spherically symmetric perfect fluid (in 3+1 dimensions), including a physical solution. This physical metric can be cast as the line element ds$^{2}=-c^2\left( {\sqrt {1-x/7} \left( {1+x} \right)^{3/2}-\frac{7\beta }{192c_1 }\left( {11+2x-x^2} \right)} \right)^2dt^2+\frac{\left( {1+x} \right)}{\left( {1-x/7} \right)}dr^2+r^2d\Omega ^2$, where c=the speed of light, c$_{1}$ is a constant, and x$\equiv $c$_{1}$r$^{2}$, for c$_{1}>$0 and $\beta $ satisfying $\sim $0.0616$<$-7$\beta $/192c$_{1}<$1. This physical solution used as a stellar model provides relatively large redshifts z -- as large as 0.87 at the stellar surface, and as large as 4.05 in the interior. Modeling large redshift objects is of interest because their populations constrain cosmological models of dark energy. Another exact solution we derive is an unphysical one for zero mass, which can be cast as the line element ds$^{2}$ = -$\left[ {a+br^2} \right]^2$c$^{2}$dt$^{2}$ + dr$^{2}$ + r$^{2}$d$\Omega ^{2 }$ for constants a and b. Although values of b$\ne $0 are unphysical, this metric is potentially interesting because it provides another classical way (apart from the introduction of a cosmological constant) to generate finite pressure everywhere in space, in a system of zero net mass. [Preview Abstract] |
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