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Title: | 論四維共形反常下的量子黑洞 On Quantum Black Holes with 4D Weyl Anomaly |
Authors: | 廖根逸 Keng-Yi Liao |
Advisor: | 賀培銘 Pei-Ming Ho |
Keyword: | 黑洞,共形物質場,共形異常,黑洞熵,半古典愛因斯坦方程, Black Hole,Conformal Matter Field,Weyl Anomaly,Entropy,Semi-classical Einstein Equation, |
Publication Year : | 2023 |
Degree: | 碩士 |
Abstract: | 我們考慮半經典愛因斯坦方程式下的共形物質場,並研究四維球對稱靜態黑洞的內部幾何結構。通過假設一個狀態方程和考慮四維共形反常,我們解愛因斯坦方程式的跡,因為它是與幾何和量子態無關。我們透過兩個步驟分析了解空間的全局結構。首先,我們在解空間中確定了3個漸近解和它們的局部行為。然後,我們通過數值求解全局結構來確定隨著r增加解空間內的流動。在獲得我們了解解空間的完整行為之後,我們加入物理邊界條件,並展示了黑洞的普遍結構,包括黑洞表面附近近普朗克曲率的密集部分和底部的殼層結構。表面下的殼層結構提供了各種可能的型態。同時,透過我們的模型,我們可以確定黑洞內部型態變化的最小長度。以此為基礎,我們計算出,因為這個結構的存在,使得熵的形式與黑洞熵符合。此外,我們也給出證據證明此結構的不是靜止的。 We consider the semi-classical Einstein equation for conformal matter fields and mainly study the interior geometry of 4D spherical static black holes. By adopting an equation of state and 4D Weyl anomaly, we solve the trace of the Einstein equation, which is geometric and state independent. We analyze the solution space in two steps. First, we identify 3 asymptotic solutions and their local behaviors in the solution space. Then, we numerically find the transition between those asymptotic solutions. After obtaining a full picture of the solution space of our setup, we then apply the physical boundary conditions, and show some possible structures of black holes, which consists of a dense part with near-Planckian curvatures at the surface and shell structures beneath. The shell structure below the surface provides a variety patterns. By considering the most probable set of patterns, we recover the entropy area law. In addition, we also show that the internal structures are time dependent. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88576 |
DOI: | 10.6342/NTU202302515 |
Fulltext Rights: | 同意授權(全球公開) |
Appears in Collections: | 物理學系 |
Files in This Item:
File | Size | Format | |
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ntu-111-2.pdf | 2.18 MB | Adobe PDF | View/Open |
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