3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item A quantum mechanical toy model for black holes(2018) Cannell, Regan WThe main aim of this dissertation is to investigate properties of the entropy of black holes. Our primary goal is to investigate the microstates of black holes. Our secondary goal is to study decoherence within the context of black holes. The methodology employed is to study simple, exactly solvable quantum models. These quantum models should serve as toy models for black holes. We consider exactly solvable quantum systems which have a non-degenerate energy spectrum. The energy levels of these quantum systems should not be equally spaced. By choosing an appropriate class of observables, we calculate the expectation values of these observables for different states within a suitably chosen ensemble. This is where the notion of quantum typicality arises. By comparing the expectation values of the chosen observable for several states within the ensemble, we discover that it is not always possible to distinguish among the several states. These findings are then generalised to the microstates of black holes, i.e. no measurement can distinguish black hole microstates. We then study the coherent and squeezed states of a simple quantum system. We deduce that even for such states, distinguishability is not possible. Finally, we study decoherence within the context of black holes. We find a simple quantum model that exhibits decoherence. We conclude that spacetime fluctuations can cause decoherence in quantum systems. Furthermore, by treating Hawking radiation as an effect of decoherence, we conclude that no information is lost in a black hole.Item Quasinormal modes for a spin-3/2 field in a reissner-Nordstrom background(2017) Ngcobo, Xolane IgnitiousIn this dissertation I will present quasinormal mode results calculated using two approximation methods; the Wentzel-Kramers-Brillouin (WKB) and the Asymptotic iteration method (AIM). I will rst do two brief examples, where we will compute the QNMs for a scalar eld in a Schwarzschild and Reissner-Nordstr=om background, then the QNMs for a massless Dirac spinor in a Schwarzschild background. These two examples will help build some intuition leading up to the main subject of this dissertation - the spin-3/2 field. The use of the WKB method is motivated by the works of Sai Iyer and Clifford M. Will [1], where they applied the WKB approximation method to computing the QNMs for black holes perturbed by fields. The AIM approximation method used here is the improved AIM approach of Cho et al [2]. This work is aimed at understanding the behaviour of spin-3/2 fi eld in a blackhole background, and since the Schwarzschild background for the spin-3/2 has been intensively studied, I have decided that the Reissner-Nordstrom background will be very interesting to study as it is a charged background.Item Quasinormal modes for spin-3/2 particles in N-dimensional Schwarzschild black hole space times(2016) Harmsen, Gerhard ErwinThis dissertation will focus on spin-3/2 perturbations on N-dimensional Schwarzschild black holes, with the aim of calculating the numerical values for the quasi-normal modes (QNMs) and absorption probabilities associated with these perturbations. We begin by determining the spinor-vector eigenmodes of our particles on an (N-2)-dimensional spherical background. This allows us to separate out the angular part and radial part on our N-dimensional Schwarzschild metric. We then determine the equations of motion and e ective potential of our particles near the N-dimensional black hole. Using techniques such as the Wentzel-Kramers-Brillouin and Improved Asymptotic Iterative Method we determine our QNMs and absorption probabilities. We see that higher dimensional black holes emit QNMs with larger real and imaginary values, this would imply they emit higher energy particles but that these particles are highly dampened and therefore would be di cult to detect. The results of the QNMs make sense if we also consider the e ective potential surrounding our black holes with the potential function increasing with increasing number of dimensions.Item Firewall argument for acoustic black holes(2015-06-08) Pontiggia, Luca TerzioWe investigate the rewall paradox proposed by AMPS [1] by rst explaining the Information Paradox together with Hawking's derivation of the thermal radiation emitted from a evaporating black hole [28]. We then ask if one can apply arguments similar to that of Hawking and AMPS in the regime of uid mechanics, which was rst considered by Unruh [59]. We assume that a black hole, with a geometry conformal to the Schwarzschild metric, can be formed in a uid. The sonic hole or \dumb" hole, which is characterized by an acoustic event horizon, is the locus of points at which the background uid is traveling at the local speed of sound. Since sound disturbances are coupled to the background uid and travel at the speed of sound, the acoustic event horizon a ects sound disturbances in a manner analogous to how gravitational black holes a ect light [62]. Like a gravitational black hole, which evaporates by emitting Hawking radiation, we check if an acoustic black hole will emit in a similar kind of radiation in the form of phonons. This is done by constructing a massless scalar eld describing phonon propagation and treating the acoustic black hole just like a gravitational black hole. We apply the arguments put forth by Hawking and AMPS and see if there is any validity to an \acoustic rewall" as this would require certain physical phenomena emerging from sub-atomic scales.Item The hidden conformal symmetry and quasinormal modes of the four dimensional Kerr black hole(2012-08-27) Jordan, BlakeThis dissertation has two areas of interest with regard to the four dimensional Kerr black hole; the rst being its conformal nature in its near region and second it characteristic frequencies. With it now known that the scalar solution space of the four dimensional Kerr black hole has a two dimensional conformal symmetry in its near region, it was the rst focus of this dissertation to see if this conformal symmetry is unique to the near region scalar solution space or if it is also present in the spin-half solution space. The second focus of this dissertation was to explore techniques which can be used to calculate these quasinormal mode (characteristic) frequencies, such as the WKB(J) approximation which has been improved from third order to sixth order recently and applied to the perturbations of a Schwarzschild black hole. The additional correction terms show a signi cant increase of accuracy when comparing to numerical methods. This dissertation shall use the sixth order WKB(J) method to calculate the quasinormal mode frequencies for both the scalar and spin-half perturbations of a four dimensional Kerr black hole. An additional method used was the asymptotic iteration method, a relatively new technique being used to calculate the quasinormal mode frequencies of black holes that have been perturbed. Prior to this dissertation it had only been used on a variety of Schwarzschild black holes and their possible perturbations. For this dissertation the asymptotic iteration method has been used to calculate the quasinormal frequencies for both the scalar and spin-half perturbations of the four dimensional Kerr black hole. The quasinormal mode frequencies calculated using both the sixth order WKB(J) method and the asymptotic iteration method were compared to previously published values and each other. For the most part, they both compare favourably with the numerical values, with di erences that are near negligible. The di erences did become more apparent when the mode number (or angular momentum per unit mass increased), but less so when the angular number increased. The only factor that separates these two methods signi cantly, was that the computational time for the sixth order WKB(J) method is less than than that of the asymptotic iteration method.