Theses and Dissertations from UMD
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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
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Item Thermodynamics of quantum gravitational ensembles(2023) Banihashemi, Batoul; Jacobson, Theodore A; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The discovery of black hole thermodynamics and its extension to cosmological horizonsdemonstrated a deep connection between thermodynamics and the nature of spacetime as a quantum system. It is then of great importance to properly understand the statistical mechanics of gravitational systems with horizon from first principles. While employing a partition function and the gravitational “Euclidean path integral” produces the expected physical result for entropy, a number of fundamental questions about the underlying analysis persist. This dissertation sharpens and resolves some puzzles regarding statistical mechanics of gravitational ensembles and the gravitational path integral, with a focus on cosmological horizons and de Sitter space. The main questions addressed in this dissertation are: how is the entropy of de Sitterspace derived in absence of any boundary on which the statistical ensemble can be properly defined? What is the correct interpretation of the first law of de Sitter horizon, according to which the horizon area shrinks upon adding matter in de Sitter static patch? And finally, can entropy of horizon-bounded systems be derived from a Hamiltonian approach and phase space path integral, without the trickery of the gravitational Euclidean path integral? The first two questions are answered by introducing an artificial boundary in the system on which a gravitational ensemble can be properly defined. Once the ensemble is defined, the semiclassical approximation of the statistical partition function yields the entropy, and the interpretation of the de Sitter first law becomes clear by identifying the system energy as the quasilocal energy defined on the boundary. To tackle the last question, the real-time phase space path integral is utilised in the Hamiltonian formulation which maintains connection to the Hilbert space of the system, and it is found that the horizon entropy is derived from a nearly Lorentzian configuration.Item Numerical studies on new techniques for gravitational wave extraction and binary black hole simulations(2009) Pazos, Enrique; Tiglio, Manuel; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation presents numerical studies of gravitational waves produced by black holes in two scenarios: perturbations of a single black hole, and the collision of a binary pair. Their detection plays a crucial roll in further testing General Relativity and opens a whole new field of observational astronomy. First, a technique called Cauchy--perturbative matching is revisited in one dimension through the use of new numerical methods, such as high order finite difference operators, constraint-preserving boundary conditions and, most important, a multi-domain decomposition (also referred to as multi-patch, or multi-block approach). These methods are then used to numerically solve the fully non-linear three-dimensional Einstein vacuum equations representing a non-rotating distorted black hole. In combination with a generalization of the Regge-Wheeler-Zerilli formalism, we quantify the effect of the background choice in the wave extraction techniques. It is found that a systematic error is introduced at finite distances. Furthermore, such error is found to be larger than those due to numerical discretization. Subsequently, the first simulations ever of binary black holes with a finite-difference multi-domain approach are presented. The case is one in which the black holes orbit for about twelve cycles before merging. The salient features of this multi-domain approach are: i) the complexity of the problem scales linearly with the size of the computational domain, ii) excellent scaling, in both weak and strong senses, for several thousand processors. As a next step, binary black hole simulations from inspiral to merger and ringdown are performed using a new technique, turduckening, and a standard finite difference, adaptive mesh-refinement code. The computed gravitational waveforms are compared to those obtained through evolution of the same exact initial configuration but with a pseudo-spectral collocation code. Both the gravitational waves extracted at finite locations and their extrapolated values to null infinity are compared. Finally, a numerical study of generic second order perturbations of Schwarzschild black holes is presented using a new gauge invariant high order perturbative formalism. A study of the self-coupling of first order modes and the resulting radiated energy, in particular its dependence on the type of initial perturbation, is detailed.