Bulletin of the American Physical Society
2009 APS April Meeting
Volume 54, Number 4
Saturday–Tuesday, May 2–5, 2009; Denver, Colorado
Session G11: Gravitational Collapse and Theoretical Relativity |
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Sponsoring Units: GGR Chair: Eric Poisson, University of Guelph Room: Plaza Court 1 |
Sunday, May 3, 2009 8:30AM - 8:42AM |
G11.00001: Small scale structure in the approach to the singularity David Garfinkle, Frans Pretorius, Woei Chet Lim, Lars Andersson Both numerical simulations and analytic approximations are presented for the small scale structure (sometimes called spikes) that arises in the approach to generic spacetime singularities. [Preview Abstract] |
Sunday, May 3, 2009 8:42AM - 8:54AM |
G11.00002: BKL Explorer: a tool to simulate the phenomenology of the BKL conjecture Beverly K. Berger Long ago, Belinskii, Khalatnikov, and Lifshitz (BKL) argued that the approach to the singularity in generic gravitational collapse behaved locally as a spatially homogeneous cosmology that was either velocity dominated (Kasner-like) or oscillatory (Mixmaster-like). This means that, operationally, in a numerical simulation of generic collapse, the PDE's of general relativity can be replaced at each spatial point by ODE's describing either the Kasner or Mixmaster cosmology. Numerical simulations of collapse in spatially inhomogeneous cosmologies support this argument. This suggests that, if one assumes this BKL conjecture to be true, one could explore the phenomenology of generic collapse by evolving, e.g., Mixmaster equations on a spatial grid with spatially dependent (smooth) initial conditions. The well known sensitivity to initial conditions would then be expected to yield an interesting, and potentially informative, visualization of the approach to the singularity. While this BKL regime is reached at different (BKL) time for different spatial points, it is likely that sufficiently close to the singularity, almost all (i.e., except at a set of measure zero) spatial points are in this regime. An algorithm originally developed by Garfinkle will be used to generate each local Mixmaster evolution. Results in one spatial dimension will be presented along with comparison to genuine spatially inhomogeneous simulations. [Preview Abstract] |
Sunday, May 3, 2009 8:54AM - 9:06AM |
G11.00003: Critical Collapses in Neutron Star Systems Kejian Jin, Wai-Mo Suen Recently we reported that neutron star systems described by a polytropic equation of state (EOS) (with polytropic index $\Gamma=2$) may undergo gravitational collapses exhibiting type I critical phenomena (Jin and Suen, Phys. Rev. Lett. vol 98, 131101, 2007). In this talk we review and discuss interesting properties of this critical phenomena, including that the critical solutions of the system has a minimum rest mass. Both increasing or decreasing the kinetic/thermal energy in the system will lead to a critical solution with higher rest mass. For $\Gamma=2$, the minimum mass value is 1.6378 ${M_\odot}$ in the absence of angular momentum. We also report on the finding of similar type I critical phenomena with non-zero angular momentum. [Preview Abstract] |
Sunday, May 3, 2009 9:06AM - 9:18AM |
G11.00004: Critical Gravitational Collapses in Neutron Star Like Systems Mew-Bing Wan, Ke-Jian Jin, Wai-Mo Suen We study the critical solution of neutron star like system previously found (Jin and Suen (2007)). In particular we show that the solution is a semi-attractor in the threshold plane separating the black hole phase and the neutron star phase. We find interesting space time and hydrodynamic properties of the solution. [Preview Abstract] |
Sunday, May 3, 2009 9:18AM - 9:30AM |
G11.00005: Spatially-Homogeneous Vlasov-Einstein Cosmology James Friedrichsen, T. Okabe, P.J. Morrison, L.C. Shepley The evolution of anisotropy in the Bianchi cosmological models, which are a set of spatially homogeneous solutions to the Einstein field equations classified by the three-dimensional Lie algebra that describes the symmetry group of the model, is studied due to the influence of matter as described by the Vlasov equation. The Einstein equations for the Bianchi models reduce to a set of coupled ordinary differential equations due to the spatial homogeneity of the models. The class A Bianchi models admit a Hamiltonian formulation in which the components of the metric tensor are the canonical coordinates. It is known that the evolution of anisotropy in the vacuum Bianchi models is determined by a potential due to the curvature of the model according to its symmetry. Matter potentials are obtained by first introducing a new matter action principle for the Vlasov equation in terms of a conjugate pair of functions and then enforcing the symmetry of the model in order to simplify the expression of the matter potential. The resulting expressions for the matter potential is given in terms of the phase space density, which is further simplified by the assumption of cold streaming matter. A qualitative difference is found in the dynamics of the non-trivial vacuum class A Bianchi models and the Bianchi Type I models with cold streaming Vlasov matter potentials that are analogous to the curvature potentials of the corresponding vacuum models. [Preview Abstract] |
Sunday, May 3, 2009 9:30AM - 9:42AM |
G11.00006: Quasilocal Energy of FRW Universe Marcus Afshar The quasilocal energy of an arbitrary FRW model of the universe is calculated. The results have the correct behavior in the small-sphere limit. Higher order corrections are found when comparing these results to classical calculations of cosmological energy. This example is unique in that it involves a non-stationary spacetime. As previous definitions are inadequate, a more precise definition of quasilocal energy is provided to accommodate non-stationary spacetimes. [Preview Abstract] |
Sunday, May 3, 2009 9:42AM - 9:54AM |
G11.00007: Self-force in compact binaries using the effective field theory approach Chad Galley We present our recent progress applying the effective field theory (EFT) approach to extreme mass ratio compact binaries (LISA sources) undergoing self-force from the backreaction of emitted gravitational waves. We focus our attention on the second order self-force on the small compact object and the corresponding emitted gravitational waves, which are both needed for doing precision gravitational wave astronomy with LISA. We also present recent work in applying the EFT approach to LIGO sources, time permitting. [Preview Abstract] |
Sunday, May 3, 2009 9:54AM - 10:06AM |
G11.00008: Gravitational Lorenz gauge self-force calculations in the time domain in 2+1D: progress report Kristen Lackeos, Leor Barack, Gaurav Khanna, Lior M. Burko The goal of this project is to calculate the self force acting on a point particle in motion in the spacetime of a Kerr black hole. Already in vacuum the problem presents several challenges, e.g., gauge-condition violating unstable modes. We decompose the field into separable azimuthal $m$-modes, although for each $m$-mode all 10 fields are coupled. Individual $m$-modes of the metric perturbations diverge logarithmically (in the proper distance from the point particle), and practical regularization may be done using a ``puncture function." This approach has several advantages, e.g. the amenability to numerical solutions in the time domain, thus benefiting from experience gained by several groups in the numerical solution of linearized wave equations on a Kerr background, and the adaptability to more complex orbits, including generic ones. We first implement this program for the simpler context of circular orbits in Schwarzschild, without exploiting the spherical symmetry of the Schwarzschild backgound or the symmetry of the orbit. Instead, we construct the scheme so that generalizations to either more complex orbits or to Kerr spacetime are susceptible of implementation at later stages, and work in 2+1D. This talk is on work still ongoing. [Preview Abstract] |
Sunday, May 3, 2009 10:06AM - 10:18AM |
G11.00009: ABSTRACT WITHDRAWN |
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