- 學位論文
第一原理方法處理資訊遺失悖論
A First Principle Approach toward the Resolution of the Information Loss Paradox
摘要
本作彙整作者已發表與正在撰寫的論文。 資訊遺失悖論作為黑洞半古典近似的最高成就，常被視為通往量子重力理論的重要關卡。霍金透過古典時空中的量子場論計算發現黑洞會釋放熱輻射，但根據么正性這些輻射必須與某種物理實體纏結。唯一合理的目標即為黑洞本身。這意味著因能量守恆逐漸蒸發的黑洞須儲存大量的熵。此悖論導致黑洞蒸發過程無法同時遵守么正性、局域性與廣義協變性這三個現代物理基本假設。 根據上述三項基本假設，我們引入一個巨觀有效模型來內蘊包含黑洞蒸發的自洽模型。在這過程中我們引入用來儲存額外熵的「隱藏區域」作為移除悖論的代價。我們著重在維持自洽所需的「隱藏區域」–黑洞交互作用。即便此模型的描述力極為強大，我們仍能定性分析可能的模型參數，並更進一步引入微觀能態密度進行解釋。這其中尤以對應到紅外極限額外熵的類零頻極點結構最為有趣。此概念本便存在於廣異相對論中。這種俗稱黑洞軟髮的系統具有豐富的物理意義。兩相對照我們認為軟髮唯有偏離零頻極限才能參與黑洞蒸發。 零頻軟髮自誕生以降便充滿爭議。最主要的反詰是軟髮遠離場源後與構成阿貝爾群的一組座標變換相當，故無法儲存熵。我們引入兩種軟髮的動態延伸，其一對應到非均向類光流的反作用力，另一則為帶有督卜勒位移與盎茹效應的座標變換。兩者協同可以在整個流形上精確地植入軟髮。這使得我們可以對黑洞視界作非微擾分析，並發現其形狀與對應到霍京溫度的表面重力會獲得非同時相依的修正。這意味著視界上出現了新的二維自由度，部分實現了之前所宣稱動態軟髮做為資訊遺失悖論解決之道的可能性。
並列摘要
This dissertation is based on previous and current projects. As a crowning achievement of the semi-classical analysis of black hole, the information loss paradox is often considered a gateway toward quantum gravity. The paradox suggests that while derived from quantum field theory in curved spacetime, the Hawking evaporation process inevitably leads to an enormous amount of entanglement entropy between an evaporated BH and the radiation it released, thus violating one or more of the following fundamental assumptions in modern physics: unitarity, locality, and general covariance. Based on the discretized horizon picture, we introduce a macroscopic effective model of the horizon area quanta that encapsulates the features necessary for black holes to evaporate consistently. The price to pay is the introduction of a ``hidden sector'' that represents our lack of knowledge about the final destination of the black hole entropy. We focus on the peculiar form of the interaction between this hidden sector and the black hole enforced by the self-consistency. Despite the expressive power of the model, we arrive at several qualitative statements. Furthermore, we identify these statements as features inside the microscopic density of states of the horizon quanta. In particular, there exists a zero-frequency-pole-like structure that corresponds to the amount of excess entropy at IR limit. Interestingly, a nontrivial IR structure naturally exists in general relativity. This ``soft hair,'' coined in contrast with the usual energetic hairs of black hole by Strominger et al., carries very rich physics. We relate these two structures, and argue that we should consider deviating away from the zero frequency limit for soft hairs to participate in the black hole evaporation. The exactly-zero-frequency soft hair, has been challenged since its birth, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any entropy. We introduce two different time-dependent extensions of the soft hair, where one is the backreaction of an anisotropic null flow, and the other is a coordinate transformation that produces the Unruh effect and a Doppler shift to the Hawking radiation spectrum. Together, they form an exact charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose shape and the associated surface gravity, i.e. the Hawking temperature, are found to be modified non-temporally, suggesting the emergence of a new 2-D degree of freedom on the horizon, thus partially fulfilling our original claim that dynamical soft hairs is potentially a way out of the inforamtion loss paradox.