Theses and Dissertations from UMD
Permanent URI for this communityhttp://hdl.handle.net/1903/2
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
Browse
3 results
Search Results
Item Analytical modeling of compact binaries in general relativity and modified gravity theories(2022) Khalil, Mohammed M.; Buonanno, Alessandra; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Gravitational-wave (GW) signals from the coalescence of almost a hundred binary systems have been detected over the past few years. These observations have improved our understanding of binary black holes and neutron stars, their properties, and astrophysical formation channels. GWs also probe gravity in the nonlinear, strong-field regime, thus allowing us to search for, or constrain, deviations from general relativity. The focus of this dissertation is improving the analytical description of binary dynamics, which is important for producing accurate waveform models that can be used in searching for GW signals, inferring their parameters, and testing gravity. The research presented here can be divided into three complementary parts: 1) extending the post-Newtonian (PN) approximation for spinning binaries to higher orders, 2) improving effective-one-body (EOB) waveform models, and 3) identifying some signatures of modified gravity theories in waveforms. The PN approximation, valid for slow motion and weak gravitational field, is widely used to model the dynamics of comparable-mass binaries, which are the main GW sources for ground-based detectors. We derive PN results for spinning binaries at the third- and fourth-subleading PN orders for the spin-orbit coupling, and at the third-subleading order for the spin(1)-spin(2) coupling. We adopt an approach that combines several analytical approximation methods to obtain PN results valid for arbitrary mass ratios from gravitational self-force results at first order in the mass ratio. This is possible due to the simple mass dependence of the scattering angle in the post-Minkowskian approximation (weak field but arbitrary velocities). The EOB formalism produces accurate waveforms by combining analytical results for the binary dynamics with numerical relativity information, while recovering the strong-field test-body limit. To improve EOB models, we include spin-precession effects in the Hamiltonian up to the fourth PN order, and extend the radiation-reaction force and waveform to eccentric orbits. We also assess the accuracy of post-Minkowskian results, for both bound and scattering orbits, and incorporate them in EOB Hamiltonians. In the context of modified gravity theories, we derive the conservative and dissipative dynamics in Einstein-Maxwell-dilaton theory at the next-to-leading PN order, and compute the Fourier-domain gravitational waveform. We also develop a theory-agnostic effective-field-theory approach for describing spontaneous and dynamical scalarization: non-perturbative phenomena in which compact objects can undergo a phase transition and acquire scalar charge. We apply this approach to binary black holes in Einstein-Maxwell-scalar theory using a quasi-stationary approximation, then extend it to account for the dynamical evolution of the scalar charge, and apply it to binary neutron stars in a class of scalar-tensor theories. Improving waveform models is important for current-generation GW detectors and necessary for future detectors, such as LISA, the Einstein telescope, and Cosmic Explorer. The results obtained in this work are important steps towards that goal.Item Novel Techniques for Simulation and Analysis of Black Hole Mergers(2011) Boggs, William Darian; Tiglio, Manuel; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation consists of three research topics from numerical relativity: waveforms from inspiral mergers of black hole binaries, recoils from head-on mergers of black holes, and a new computational technique for error-reduction. The first two topics present research from journal articles that I coauthored with my colleagues in the NASA Goddard Numerical Relativity research group. Chapter 2 discusses a heuristic model of black hole binary mergers and the waveforms produced by them, based on simulations of nonspinning black holes. The gravitational radiation is interpreted as the result of an implicit rotating source that generates the radiation modes as the source multipoles rotate coherently. This interpretation of the waveform phase evolution provides a unified physical picture of the inspiral, plunge, and ringdown of the binaries, and it is the basis of an analytic model of the late-time frequency evolution. Chapter 3 presents a study of kicks in head-on black hole mergers, emphasizing the distinct contributions of spin and mass ratio, as well as their combined effects, to these radiation-induced recoils. The simpler dynamics of head-on mergers allow a more clear separation of the two types of kick and a validation of post-Newtonian predictions for the spin scaling of kicks. Finally, Chapter 4 presents a technique I developed to improve the accuracy of the field evolution in numerical relativity simulations. This "moving patches" technique uses local coordinate frames to minimize black hole motion and reduce error due to advection terms. In tests of the technique, I demonstrate reduction in constraint violations and in errors in the orbital frequency derived from the black holes' motions. I also demonstrate an accuracy gain in a new diagnostic quantity based on orbital angular momentum. I developed this diagnostic for evaluating the moving patches technique, but it has broader applicability. Though the moving patches technique has significant performance costs, these limitations are specific to the current implementation, and it promises greater efficiency and accuracy in the future.Item Numerical studies of constraints and gravitational wave extraction in general relativity(2004-08-04) Fiske, David Robert; Misner, Charles W; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Within classical physics, general relativity is the theory of gravity. Its equations are non-linear partial differential equations for which relatively few closed form solutions are known. Because of the growing observational need for solutions representing gravitational waves from astrophysically plausible sources, a subfield of general relativity, numerical relativity, has a emerged with the goal of generating numerical solutions to the Einstein equations. This dissertation focuses on two fundamental problems in modern numerical relativity: (1) Creating a theoretical treatment of the constraints in the presence of constraint-violating numerical errors, and (2) Designing and implementing an algorithm to compute the spherical harmonic decomposition of radiation quantities for comparison with observation. On the issue of the constraints, I present a novel and generic procedure for incorporating the constraints into the equations of motion of the theory in a way designed to make the constraint hypersurface an attractor of the evolution. In principle, the prescription generates non-linear corrections for the Einstein equations. The dissertation presents numerical evidence that the correction terms do work in the case of two formulations of the Maxwell equations and two formulations of the linearized Einstein equations. On the issue of radiation extraction, I provide the first in-depth analysis of a novel algorithm, due originally to Misner, for computing spherical harmonic components on a cubic grid. I compute explicitly how the truncation error in the algorithm depends on its various parameters, and I also provide a detailed analysis showing how to implement the method on grids in which explicit symmetries are enforced via boundary conditions. Finally, I verify these error estimates and symmetry arguments with a numerical study using a solution of the linearized Einstein equations known as a Teukolsky wave. The algorithm performs well and the estimates prove true both in simulations run on a uniform grid and in simulations that make use of fixed mesh refinement techniques.