Bulletin of the American Physical Society
APS April Meeting 2013
Volume 58, Number 4
Saturday–Tuesday, April 13–16, 2013; Denver, Colorado
Session H14: Numerical Investigations in Relativity |
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Sponsoring Units: GGR Chair: David Garfinkle, Oakland University Room: Plaza Court 3 |
Sunday, April 14, 2013 10:45AM - 10:57AM |
H14.00001: Relative stability of black hole threshold solutions in gravitational collapse Theodor Brasoveanu, Frans Pretorius We present numerical studies of the relative stability of critical solutions in problems of gravitational collapse. These strong-field solutions to Einstein equations, initially discovered by Matt Choptuik, arise at the threshold of black hole formation. We study the evolution of systems with multiple matter sources in spherical symmetry that exhibit the same type of threshold solution when studied individually and only interact with each other gravitationally. Given the unstable nature of critical solutions, the central question that we address is whether certain types of matter are more prone to collapse in the presence of other types of matter. Using adaptive grid techniques to solve Einstein equations coupled to matter, we notice that the near-critical solution of the combined system seems to switch from one type of threshold to another, as the critical point is approached in parameter space. So far, we have indication that massless scalar fields dominate the stability hierarchy in a mixed-matter system, but the overall dynamics depends on the relative amounts of energy present in the system and on their corresponding spatial distribution. [Preview Abstract] |
Sunday, April 14, 2013 10:57AM - 11:09AM |
H14.00002: Critical Collapse of Rotating Gravitational Waves: Recent Progress Tony Chu Critical phenomena in general relativity have received much interest since Choptuik's pioneering work on the threshold of black hole formation in the collapse of a spherically symmetric massless scalar field. By considering a one-parameter family of initial data, the scalar field configuration would either collapse to a black hole or eventually disperse, depending on whether the parameter was larger or smaller than some critical value. Furthermore, it was found that the mass of the black hole formed follows a universal power-law scaling as a function of the parameter's distance from its critical value. Shortly afterwards, similar critical phenomena in the collapse of axisymmetric gravitational waves were discovered by Abrahams and Evans. In fact, it is now thought that critical phenomena are a generic feature of gravitational collapse under fine-tuning of initial conditions. However, surprisingly little is known about situations that include angular momentum. In this talk, I will describe recent progress in simulating the collapse of rotating gravitational waves, in which the waves may carry large angular momentum, and comment on the approach to the critical solutions in these cases. [Preview Abstract] |
Sunday, April 14, 2013 11:09AM - 11:21AM |
H14.00003: Scalar Field in AdS: BHs, boson stars and collapse Steven Liebling The dynamics of a scalar field in spherically symmetric Anti-de Sitter space have attracted significant interest since the remarkable result of (Bizon \& Rostworowski, 2011) showed the existence of a weakly turbulent instability. An initial configuration of scalar field repeatedly travels outward, reflects off the AdS boundary, and implodes through the origin, all the while sharpening under the influence of gravity. In contrast, a stationary configuration of scalar field, namely a boson star, is perturbatively and numerically stable. Finally, if one turns off gravity and instead adds a nonlinear potential via the semilinear wave equation, a similar instability is seen in which even small initial data eventually collapses to form a singularity. If one instead implements a reflecting wall at some finite boundary, dispersion competes with the instability, and one finds a transition below which collapse ceases. [Preview Abstract] |
Sunday, April 14, 2013 11:21AM - 11:33AM |
H14.00004: Numerical Relativity as a tool for studying the Early Universe David Garrison Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this presentation, I show how the framework of numerical relativity can be used for studying cosmological models. We are working to develop a large-scale simulation of the dynamical processes in the early universe. These take into account interactions of dark matter, scalar perturbations, gravitational waves, magnetic fields and a turbulent plasma. The code described in this report is a GRMHD code based on the Cactus framework and is structured to utilize one of several different differencing methods chosen at run-time. It is being developed and tested on the Texas Learning and Computation Center's Xanadu cluster. [Preview Abstract] |
Sunday, April 14, 2013 11:33AM - 11:45AM |
H14.00005: Ultrarelativistic black hole formation William East, Frans Pretorius A topic in general relativity that remains poorly understood is the formation of black holes in ultrarelativistic collisions. Besides being an interesting theoretical question, it has been suggested that this may occur in the collision of cosmic rays with the Earth's atmosphere and in proton collisions at the LHC, in scenarios where large extra dimensions set the true Planck scale at around a TeV. We present results from numerical simulations of the head-on collision of equal mass particles, modeled as self-gravitating fluid spheres, obtained by solving the Einstein equations coupled to hydrodynamics. We focus on cases well within the kinetic energy dominated regime ($\gamma=8$ to 12) and find that black hole formation does occur for sufficiently large boosts. Moreover, near yet above the threshold of black hole formation, the collision initially leads to the formation of two distinct apparent horizons that subsequently merge. We argue that this can be understood in terms of a focusing effect, where one boosted particle acts as a gravitational lens on the other and vice versa, and that this is further responsible for the threshold being lower (by a factor of a few) compared to simple hoop conjecture estimate. [Preview Abstract] |
Sunday, April 14, 2013 11:45AM - 11:57AM |
H14.00006: Caustic echoes and their astrophysical applications Chad Galley, Anil Zenginoglu A source of waves (scalar, electromagnetic, or gravitational) near the event horizon of a black hole leads to the formation of a caustic on the other side of the horizon. The caustic forms from the trapping of energy by the strong curvature near the black hole and leads to echoes of the source that may have astrophysical consequences. In this talk, I briefly review the main properties of ``caustic echoes'' and discuss some potential astrophysical applications that may also be relevant for future gravitational wave searches. [Preview Abstract] |
Sunday, April 14, 2013 11:57AM - 12:09PM |
H14.00007: Intermediate behavior of Kerr Black Hole tails Anil Zengino\u{g}lu, Gaurav Khanna, Lior M. Burko The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed a puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed `splitting'. We discuss far-field splitting in the full field and near-horizon splitting in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the splitting behavior. The far-field splitting is explained by competition between projected modes. The near-horizon splitting is due to excitation of lower multipole modes that back excite the multipole mode for which splitting is observed. In both cases splitting is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. [Preview Abstract] |
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