黑洞：古典時空解之生成演算法與量子纏結島嶼

Towards a Thorough Description of Black Holes: Spacetime Generating Algorithm and Entanglement Island

邵暐翔(Wei-Hsiang Shao)

指導教授 ： 陳丕燊

國立臺灣大學/理學院/物理學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101244

摘要

近年來針對黑洞資訊悖論的研究指出了量子重力在事件視界附近發揮作用的可能性。量子重力對黑洞周圍時空結構的影響極有可能被由廣義相對論延伸出的有效修正重力理論精準地捕捉與建模，因此就理論和實驗觀測的角度而言，對於修正重力理論中時空幾何之確切了解相當迫切，特別是在最近重力波探測與黑洞剪影(shadow)觀測取得重大進展的時期；為此，本論文的第一部分致力於探究獲取各種修正重力理論中時空解析解之高效方法。本文討論了透過修正重力理論與其Einstein frame表示法之間的對應來系統化地尋求解析解之方案，結果表明，此方案得以被成功套用於其中一類涵蓋廣泛之Palatini重力與玻色物質耦合的理論。文中接著以範例演示及驗證了此求解程序之有效性，並進而得到了新的時空解，其所描述的物體為一「黑洞模擬者」(black hole mimicker)。進一步的分析顯示該物體之剪影雖具有奇特特徵，但仍與廣義相對論中Kerr旋轉黑洞之剪影極為相似。
論文的第二部分轉而聚焦黑洞的量子面向。黑洞資訊悖論的癥結在於晚期霍金輻射所攜帶的資訊量與量子力學之預期存在著巨大差異，而近期一系列與「纏結島嶼」(entanglement island)相關之研究進展聲稱能夠在不改變黑洞的傳統半古典描述之下解決這項矛盾。此篇章將闡明此想法的一些主要元素，且文中將從不同角度去論證低能量半古典架構下的「島嶼」猜想意味著在高能量子重力理論中存在大尺度非定域性(nonlocal)之交互作用。

關鍵字

古典黑洞 ； 修正重力理論 ； 量子黑洞 ； 資訊遺失悖論 ； 纏結熵

並列摘要

The black hole information paradox has hinted at the likelihood of quantum gravity coming into play in the vicinity of the event horizon. The quantum gravity effects on the classical spacetime structure around a black hole might be nicely captured and modelled by effective theories of gravity that extend beyond general relativity. Precise knowledge of the spacetime geometries in these theories are thus highly desired from both a theoretical and observational standpoint, especially in this promising era of gravitational wave detections and black hole shadow images. For this reason, Part I of the thesis is devoted to the study of an efficient method designed to obtain exact analytic spacetime solutions in various gravitational theories. An attempt at a systematic way of pursuing solutions via a dual correspondence between the gravitational theory and its Einstein frame representation is discussed. It is shown that such a procedure can be well formulated for a broad class of Palatini theories of gravity coupled to bosonic matter. Explicit example of this implementation is demonstrated, which leads to a newly discovered black hole mimicker whose shadow image displays intriguing features yet closely resembles that of a Kerr black hole.
Part II of the thesis is focused on quantum black holes as viewed by an external observer. The hallmark of the information loss paradox is the considerable discrepancy between the amount of information contained in the late­-time Hawking radiation and quantum mechanical expectations. A recent breakthrough known as the ‘island’ proposal has claimed to have offered a relief to this tension without altering the low­-energy semi-classical description of black holes. Starting from the essential ingredients of Hawking radiation, some of the main elements that underlie this proposal will be clarified. In particular, it will be argued from several aspects that the island conjecture in the infrared (IR) implies dynamics featuring large­-scale nonlocality in the ultraviolet (UV) regime.

並列關鍵字

Classical Black Holes ； Alternative Gravity Theories ； Quantum Aspects of Black Holes ； Information Loss Paradox ； Entanglement Entropy

參考文獻

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