ItemCausal Differencing in ADM and Conformal ADM Formulations: A Comparison in Spherical Symmetry.(Physical Review D. Volume 62, 2000) Garrison, DavidBlack hole excision is at present the most promising approach to deal with the singularities in black hole spacetimes. The implementation of this technique is done through carefully designed algorithms that exploit the causal structure of the spacetime in the black hole region. Causal differencing has shown to be one of the promising algorithms. To date, it has only been actively implemented in the Arnowitt-Deser-Misner (ADM) and Einstein-Bianchi 3+1 formulations of the Einstein equations. Recently, an approach closely related to the ADM one, commonly referred to as “conformal ADM” (CADM) method has shown excellent results when modeling waves on flat spacetimes and black hole spacetimes where singularity avoiding slices are used to deal with the singularity. In these cases, the use of the CADM method has yielded longer evolutions and better outer boundary dependence than those obtained with the ADM one. If this success translates to the case where excision is implemented, then the CADM formulation will likely be a prime candidate for modeling generic black hole spacetimes. In the present work we investigate the applicability of causal differencing to the CADM method, presenting the equations in a convenient way for such a task. We investigate whether the causal differencing implementation already developed for the ADM system can be extended to the CADM one. ItemBlack Hole Spectroscopy: testing general relativity through gravitational-wave observations(Classical and Quantum Gravity 21, 2004) Garrison, DavidAssuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible charge-to-mass ratio, the black hole quasi-normal mode spectrum is characterized entirely by the black hole mass and angular momentum and is unique to black holes. In a different theory of gravity, or if the observed radiation arises from a different source (e.g., a neutron star, strange matter or boson star), the spectrum will be inconsistent with that predicted for general relativistic black holes. We give a statistical characterization of the consistency between the noisy observation and the theoretical predictions of general relativity, together with a numerical example. ItemGravity Gradients in LIGO: a proposal for Data Analysis(Proceedings of the Tenth Marcel Grossman Meeting on General Relativity, 2006) Garrison, DavidWe propose a method to analyze seismic noise data to bound the influence of gravitational gradients affecting the sensitivity of gravitational wave detectors. We present results obtained with data taken at the LIGO Hanford Observatory. The data shows that the method is useful, and also suggests local sources of gravitational gradients. ItemNumerical analysis of simplified Relic-Birefringent gravitational waves(Classical and Quantum Gravity 24, 2004) Garrison, DavidSome theories suggest that gravitational waves created in the early universe may be observable with future gravitational wave interferometers. As a result, identifying the characteristics of these gravitational waves and their corresponding power spectrums at different epochs has become an important area of study. The general solutions to these equations can become quite complex, making the task of obtaining analytical results a difficult one without simplifying assumptions. Using numerical techniques, a general solution to the birefringent gravitational wave equation is explored. This form of the gravitational wave equation is partly composed of a mode function that resembles the Coulomb wave equation from quantum mechanics, which has been explored computationally in the past. An attempt is then made to numerically solve these equations and the corresponding power spectrum for the present universe. Current/planned observatories such as LISA and Advanced LIGO can test these results. ItemTESTING BINARY BLACK HOLE CODES IN STRONG FIELD REGIMES: UNDERSTANDING NUMERICAL INSTABILITIES THROUGH COMPUTATIONAL EXPERIMENTS(LAP Lambert Academic Publishing, 2011) Garrison, DavidIn order to further our understanding of the instabilities which develop in numerical relativity codes, I study vacuum solutions of the cosmological type (T^3 topology). Specifically, I focus on the 3+1 ADM formulation of Einsteins equations. This involves testing the numerical code using the following non-trivial periodic solutions, Kasner, Gowdy, Bondi and non-linear gauge waves. I look for constraint violating and gauge mode instabilities as well as numerical effects such as convergence, dissipation and dispersion. I will discuss techniques developed to investigate the stability properties of the numerical code. ItemWhat Every Successful Physics Graduate Student Should Know(Smashwords, 2013) Garrison, DavidThis guide is intended for students who are considering pursuing a graduate school program in physics. I chose the title, “What Every Successful Physics Graduate Student Should Know” because I honestly believe that if you want to be successful in a graduate physics program, the information contained in these pages will be of great value to you. The motivation for the creation of this guide originated with a suggestion from one of my students who felt that this could provide a useful aid to people who are interested in pursuing a graduate-level physics degree. It is written in such a way that it applies to graduate physics programs in general and not only the University of Houston Clear Lake (UHCL) Physics program. ItemA Numerical Simulation of Chern-Simons Inflation(Advances in Astronomy, 2013) Garrison, DavidIn this work, we present results of numerical simulations of the Chern-Simons Inflation Model proposed by Alexander, Marciano and Spergel. According to this model, inflation begins with a fermion condensate interacting with a gauge field. Crucial to the success of this mechanism is the assumption that the Chern-Simons interaction would drive energy from the initial random spectrum into a narrow band of frequencies at superhorizon scales. In this work we numerically confirm this expectation. These gauge fields and currents, when combined with the Friedmann equations, were broken into a system of hyperbolic equations and numerically simulated. It was found in our simulation that, by including the effects of the chiral anomaly for the axial vector current, inflation ended satisfactorily after approximately 60 e-folds. ItemNumerical Relativity as a tool for studying the Early Universe(Journal of Gravity, 2014) Garrison, DavidNumerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological models. The author is 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 dynamic 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. ItemInvariants in Relativistic MHD Turbulence(Journal of Modern Physics, 2016) Garrison, DavidThe objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants in the relativistic case and comparing them to what we know of nonrelativistic turbulence. Although much work has been done to understand the dynamics of nonrelativistic systems (mostly for ideal incompressible fluids), there is minimal literature explicitly describing the dynamics of relativistic MHD turbulence using numerical simulations. Many researchers simply assume that relativistic turbulence has the same invariants and obeys the same dynamics as non-relativistic systems our results show that this assumption may be incorrect. ItemExtracting Gravitational Waves Induced by Plasma Turbulence in the Early Universe through an Averaging Process(Classical and Quantum Gravity 34, 2017) Garrison, DavidThis work is a follow-up to the paper, "Numerical Relativity as a Tool for Studying the Early Universe". In this article, we determine if cosmological gravitational waves can be accurately extracted from a dynamical spacetime using an averaging process as opposed to conventional methods of gravitational wave extraction using a complex Weyl scalar. We calculate the normalized energy density, strain and degree of polarization of gravitational waves produced by a simulated turbulent plasma similar to what was believed to have existed shortly after the electroweak scale. This calculation is completed using two numerical codes, one which utilizes full General Relativity calculations based on modified BSSN equations while the other utilizes a linearized approximation of General Relativity. Our results show that the spectrum of gravitational waves calculated from the nonlinear code using an averaging process are nearly indistinguishable from those calculated from the linear code. This result validates the use of the averaging process for gravitational wave extraction of cosmological systems.