Colliding black holes with linearized gravity

We give a brief summary of results and ongoing research in the application of linearized theory to the study of black hole collisions in the limit in which the holes start close to each other. This approximation can be a valuable tool for comparison and code-checking of full numerical relativity computations. The approximation works quite well for the head-on case and this is motivation to pursue its use in other more interesting contexts. We summarize current efforts towards establishing the domain of validity of the approximation and its use in generation and evolution of initial data for more interesting physical cases.Comment: 4 pages, RevTeX, 2 figures included with epsf, to appear in the Proceedings of the Sixth Canadian Conference on General Relativity and Relativistic Astrophysic

Perturbations of the Kerr spacetime in horizon penetrating coordinates

We derive the Teukolsky equation for perturbations of a Kerr spacetime when the spacetime metric is written in either ingoing or outgoing Kerr-Schild form. We also write explicit formulae for setting up the initial data for the Teukolsky equation in the time domain in terms of a three metric and an extrinsic curvature. The motivation of this work is to have in place a formalism to study the evolution in the ``close limit'' of two recently proposed solutions to the initial value problem in general relativity that are based on Kerr-Schild slicings. A perturbative formalism in horizon penetrating coordinates is also very desirable in connection with numerical relativity simulations using black hole ``excision''.Comment: 8 pages, RevTex, 2 figures, final version to appear in CQ

Unified model of loop quantum gravity and matter

We reconsider the unified model of gravitation and Yang--Mills interactions proposed by Chakraborty and Peld\'an, in the light of recent formal developments in loop quantum gravity. In particular, we show that one can promote the Hamiltonian constraint of the unified model to a well defined anomaly-free quantum operator using the techniques introduced by Thiemann, at least for the Euclidean theory. The Lorentzian version of the model can be consistently constructed, but at the moment appears to yield a correct weak field theory only under restrictive assumptions, and its quantization appears problematic.Comment: 4 pages, dedicated to Michael P. Ryan on the occasion of his sixtieth birthda

Flow structure in a model of aircraft trailing vortices

We consider a model of incompressible trailing vortices consisting of an array of counter-rotating structures in a doubly periodic domain, infinite in the vertical direction. The two-dimensional vortex array of Mallier and Maslowe is combined with an axial velocity profile chosen proportional to the initial axial vorticity to provide an initial condition for the vortex wake. This base flow is a weak solution of the steady Euler equations with three velocity components that are functions of two spatial coordinates, thus allowing its linear stability properties to be investigated. These are used to interpret several stages in the development of vortex structure observed in fully three-dimensional direct numerical simulation (DNS) at Reynolds numbers Gamma/(2pinu)=[script O](1000). For sufficiently high axial velocity, its effect can be seen, in that each vortex in the linear array first develops helical structures before undergoing a period of relaminarization. At later times the more slowly growing cooperative elliptical instabilities become apparent, but the helical structure persists and the observed vortical structures remain coherent for longer periods than in the absence of axial velocity. Using the stretched-vortex subgrid model, large-eddy simulation runs are performed at large Reynolds numbers and a mixing transition identified at about Re=1–2×10^4. Similar phenomena are observed in these simulations as are seen in the DNS

Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations

We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate

Large quantum gravity effects: backreaction on matter

We reexamine the large quantum gravity effects discovered by Ashtekar in the context of 2+1 dimensional gravity coupled to matter. We study an alternative one-parameter family of coherent states of the theory in which the large quantum gravity effects on the metric can be diminished, at the expense of losing coherence in the matter sector. Which set of states is the one that occurs in nature will determine if the large quantum gravity effects are actually observable as wild fluctuations of the metric or rapid loss of coherence of matter fields

Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock

Large-eddy simulations of the Richtmyer–Meshkov instability with reshock are pre- sented and the results are compared with experiments. Several configurations of shocks initially travelling from light (air) to heavy (sulfur hexafluoride, SF6) have been simulated to match previous experiments and good agreement is found in the growth rates of the turbulent mixing zone (TMZ). The stretched-vortex subgrid model used in this study allows for subgrid continuation modelling, where statistics of the unresolved scales of the flow are estimated. In particular, this multiscale modelling allows the anisotropy of the flow to be extended to the dissipation scale, eta, and estimates to be formed for the subgrid probability density function of the mixture fraction of air/SF6 based on the subgrid variance, including the effect of Schmidt number