Browsing by Subject "relativity"
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Item Application Of The Cubed-Sphere Grid To Tilted Black Hole Accretion Disks(2009-01) Fragile, P. Chris; Lindner, Christopher C.; Anninos, Peter; Salmonson, Jay D.; Lindner, Christopher C.In recent work we presented the first results of global general relativistic magnetohydrodynamic (GRMHD) simulations of tilted (or misaligned) accretion disks around rotating black holes. The simulated tilted disks showed dramatic differences from comparable untilted disks, such as asymmetrical accretion onto the hole through opposing "plunging streams" and global precession of the disk powered by a torque provided by the black hole. However, those simulations used a traditional spherical-polar grid that was purposefully under-resolved along the pole, which prevented us from assessing the behavior of any jets that may have been associated with the tilted disks. To address this shortcoming we have added a block-structured "cubed-sphere" grid option to the Cosmos++ GRMHD code, which will allow us to simultaneously resolve the disk and polar regions. Here we present our implementation of this grid and the results of a small suite of validation tests intended to demonstrate that the new grid performs as expected. The most important test in this work is a comparison of identical tilted disks, one evolved using our spherical-polar grid and the other with the cubed-sphere grid. We also demonstrate an interesting dependence of the early-time evolution of our disks on their orientation with respect to the grid alignment. This dependence arises from the differing treatment of current sheets within the disks, especially whether or not they are aligned with symmetry planes of the grid.Item Book Review of Discovering Relativity for Yourself by Sam Lilley(Library Journal, 1981-07-01) Sandy, John H.Item Signal Processing Compact Binary Coalescence Gravitational Wave Data from the Advanced LIGO Detectors(2017-12) Bogat, Sophia E.; Matzner, RichardAbstract or description: This thesis explores the complex signal processing tools and techniques used to perform gravitational wave astronomy. The first ever direct observation of spatial strain caused by a gravitational wave was achieved by the Laser Interferometer Gravitational-Wave Observatory (LIGO) on September 14th, 2015, nearly 100 years after Albert Einstein predicted their existence. Because the amplitude of the strain is so small (on the order of 10-21), it must be measured by a 4 kilometer long interferometer equipped with extremely advanced thermal and seismic vibration isolation systems. Furthermore, the data must undergo significant processing in the form of whitening, matched filtering, and bandpass filtering. We present a detailed study of the steps undergone to identify and validate potential gravitational wavesignals using the LIGO-designed PyCBC software framework for the observation of compact binary coalescence.Item Signature Changing Spacetimes and WKB Approximations in General Relativity(2015-05) Young, Sean A. Q.; Matzner, Richard A.Some properties of spacetimes that change signature from Riemannian (positive definite metric) to Lorentzian (metric has a single negative eigenvalue) are investigated. Specifically, the form of geodesics and solutions to the Klein-Gordon equation are calculated. Geodesics behave as expected since they are equally well defined for Lorentzian and Riemannian manifolds, though null geodesics cease to have meaning in the Riemannian region. Solutions to the Klein-Gordon equation exhibit oscillatory behavior in the Lorentzian region and exponential behavior in the Riemannian region. In an effort to further interpret these results, approximate wave solutions are found for a generic spacetime using WKB approximations in the large momentum limit. This approximation encompasses traditional, non-degenerate spacetimes as well as those that change signature. This solution is shown to break down near regions where the metric becomes degenerate, except in the 1 + 1 dimensional case. Further, these solutions can define a vector field with the gradient of their phase. The integral curves of the resulting field are shown to be geodesics, parametrized by an affine parameter.