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published_or_final_version / Literary and Cultural Studies / Master / Master of Arts

We employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework).  We enrich the classical scheme for metric perturbations over a curved background by also including matter fields and metric conformal fluctuations.  We show in general that a conformally modulated metric induces dephasing as a result of an effective nonlinear Newtonian potential obtained in the appropriate non-relativistic limit of a minimally coupled Klein-Gordon field.  The special case of vacuum fluctuations is considered and a quantitative estimate of the expected effect deduced. Secondly, we address the question of how conformal fluctuations could physically arise.  By applying the random gravity framework we first show that standard GR seems to forbid spontaneous conformal metric modulations.  Finally we argue that a different result follows within scalar-tensor theories of gravity such as e.g. Brans-Dicke theory. In this case a conformal modulation of the metric arises naturally as a result of the fluctuations in the Brans-Dicke field and quantum dephasing of a test particle is expected to occur.  For large negative values of the coupling parameter the conformal fluctuations may also contribute to alleviate the well known problem of the large zero point energy due to quantum matter fields.

張鳳麟. / Thesis (M.A.)--香港中文大學硏究院哲學學部. / Manuscript. / Includes bibliographical references: leaves 395-403. / Zhang Fenglin. / Thesis (M.A.)--Xianggang Zhong wen da xue yan jiu yuan zhe xue xue bu. / 導言 --- p.1 / Chapter 第一章 --- 康德對於時空問題之陳構模式 / Chapter 1 --- 在“Disserttation´ح中所提出的時空觀不同於《批判》的意義 --- p.12 / Chapter 2 --- 時空納入《批判》之〈超越感性論〉中討論 --- p.24 / Chapter 3 --- 康德對立於傳統形而上學之主客關係模式 --- p.32 / Chapter 4 --- 分析與綜合，先驗與後驗的分別和知識之可能模式 --- p.39 / Chapter 5 --- “ 知識´ح、´ح對象´ح及´ح直覺´ح之關係及其各層意義 --- p.46 / Chapter 6 --- 知識關聯於對象的最直接方式是直覺 --- p.59 / Chapter 7 --- 感性的意義為接受性之能力，可為純粹的或經驗的 --- p.66 / Chapter 8 --- 空間是純粹直覺以及直覺之形式的二重性意義 --- p.76 / 註釋 / Chapter 第二章 --- 〈超越感性論〉中時空的論證 / Chapter 1 --- 歷代哲學家對時空本質的各種看法 --- p.99 / Chapter 2 --- 時空的關係說與時空的絶對說 --- p.109 / Chapter 3 --- 康德對時空問題的陳構方式有別於牛頓及萊布尼茲 --- p.112 / Chapter 4 --- 空間為外感形式與時間為內感形式之分別 --- p.122 / Chapter 5 --- 空間之“形而上的解釋´ح之第一論證 --- p.135 / Chapter 6 --- 空間之“形而上的解釋´ح之第二論證 --- p.144 / Chapter 7 --- 空間之“形而上的解釋´ح之第三論證 --- p.149 / Chapter 8 --- 空間之“形而上的解釋´ح之第四論證 --- p.161 / Chapter 9 --- 空間之“形而上的解釋´ح之分別 --- p.171 / 註釋 / 附錄 --- p.181 / 註釋 / Chapter 第三章 --- 從時空看人的有限性 / Chapter 1 --- “超越的觀念性´ح與“經驗的實在性´ح --- p.201 / Chapter 2 --- 對象、表象和現象之分別意義及其關係 --- p.227 / Chapter 3 --- 感性直覺與智的直覺之超越區別 --- p.242 / 註釋 / Chapter 第四章 --- 空間之超越的應用──幾何學的問題 / Chapter 1 --- 空間之“超越的解釋´ح以及超越的決定 --- p.264 / Chapter 2 --- 幾何學之客觀的實在性 --- p.283 / Chapter 3 --- 歐氏空間為直覺唯一空間 --- p.295 / 註釋 / Chapter 第五章 --- 康德哲學對近代哲學挑戰之回應 / Chapter 1 --- 攻擊康德哲學之兩個代表人物 ──羅素和賴欣巴哈 --- p.304 / Chapter 2 --- 羅素對四個空間之“形而上的解釋´ح之駁難 --- p.306 / Chapter 3 --- 以眼鏡比喻時空這種主體提供之直覺形式之錯誤 --- p.322 / Chapter 4 --- 康德之幾何學意義不同於羅素之幾何學 --- p.329 / Chapter 5 --- 非歐氏幾何學的出現不能推翻康德空間說 --- p.345 / Chapter 6 --- 賴欣巴哈之幾何學意義不同於康德之幾何學 --- p.367 / Chapter 7 --- 幾何學視覺化之問題 --- p.372 / Chapter 8 --- 賴欣巴哈理解之時間不同於康德之時間意義 --- p.385 / 註釋 / 結論 --- p.392 / 參考書目 --- p.395-403

In this work, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, remain uniformly bounded and decay to a linearized Kerr metric on the exterior region. Our method employs Hodge decomposition to split the solution into closed and co-closed portions, respectively identified with even-parity and odd-parity solutions in the physics literature. For both portions, we derive Regge-Wheeler type equations for decoupled, gauge-invariant quantities at the level of perturbed connection coefficients. A general framework for the analysis of Regge-Wheeler type equations is presented, identifying sufficient conditions for decay estimates. With the choice of an appropriate gauge in each of the two portions, such decay estimates on these decoupled quantities are used to establish decay of the linearized metric coefficients, completing the proof of linear stability. The initial value problem is formulated on Cauchy data sets, complementing the work of Dafermos-Holzegel-Rodnianski [6], where the linear stability of Schwarzschild is established for characteristic initial data sets.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Jan. 5, 2010). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Department of Physics, University of Alberta." Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 125-134). Available also in a digital version from Dissertation Abstracts.

Thesis--Freie Universität Berlin. / Includes bibliographical references (p. 363-368).