博碩士論文 962402009 詳細資訊




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姓名 鄒守峻(Shou-Jyun Zou)  查詢紙本館藏   畢業系所 物理學系
論文名稱 四維黑洞的全息描述
(Holographic Descriptions of Four-dimensional Black Holes)
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摘要(中) 在這篇論文中,我們討論黑洞和共形場(CFT)之間的對應關係。根據全息原理,對應的 CFT 至少比黑洞少一個維度,就如同 AdS_D/CFT_{D-1} 的對應關係。我們分析帶電黑洞,Reissner-Nordstrom(RN)和 Kerr-Newman(KN)的情形。我們知道近視界極端 Kerr 黑洞會有(warped)AdS_3幾何結構,類似的結構也出現在當 RN 黑洞放到 5 維空間的近視界極端情形。對於 RN 黑洞的例子,CFT_2的對應描述預計也有電荷參數。我們詳細探討這類形的對應。此外,我們的研究結果還表明,有兩個自然的對應描述 KN 黑洞各自對應旋轉和電荷參數。為確認這個現象,我們討論非極端 KN 黑洞的隱性二維共形對稱性。
摘要(英) In this thesis, we discuss the correspondence between black holes and conformal field theory. According to the holographic principle, the associated dual CFT should be one-dimension less than the spacetime of black hole, as the usual AdS$_D$/CFT$_{D-1}$ correspondence. We generalize the analysis for the Kerr to the charged black holes, in particular Reissner-Nordstr"{o}m (RN) and Kerr-Newman (KN). Like a (warped) AdS$_3$ geometry appearing in the near horizon of extremal Kerr, the similar structure also shows up in the RN black hole when it is uplifted into 5D. Thus a CFT$_2$ description is expected also for the charge parameter. We explore this sector of the duality in details. Moreover, our results also suggest that there are two natural dual descriptions for the KN black holes corresponding the the associated rotating and charge parameters. To confirm this prospect, we have explored the hidden 2D conformal symmetries in the generic non-extremal KN black hole.
關鍵字(中) ★ 黑洞
★ 全息原理
★ 共形場論
關鍵字(英) ★ black hole
★ conformal field theory
★ holographic principle
論文目次 Chinese Abstract i
Abstract ii
Acknowledgements iii
contents iv
1 Introduction 1
1.1 Holographic Principle . . . . . . . . . . . . . . . . 1
1.2 The Aim of Thesis . . . . . . . . . . . . . . . . . . 5
2 The Kerr/CFT Correspondence 6
2.1 Near Horizon Geometry of Extremal Kerr . . . . . . . .6
2.2 Asymptotic Symmetry Group and Central Charge . . . . .8
2.3 Comparison of CFT and BH entropies . . . . . . . . . 11
2.4 Kerr/CFT in AdS2/CFT1Viewpoint . . . . . . . . . . . 12
2.4.1 2D effective action . . . . . . . . . . . . . . . .12
2.4.2 The solutions . . . . . . . . . . . . . . . . . . .13
2.4.3 The boundary counterterms . . . . . . . . . . . . .13
2.4.4 Asymptotic symmetries and central charge . . . . . 14
2.5 Hidden Conformal Symmetry and Conformal Weight . . . 15
2.5.1 Hidden conformal symmetry . . . . . . . . . . . . .16
2.5.2 Absorption cross section . . . . . . . . . . . . . 18
2.6 Summary and discussion . . . . . . . . . . . . . . . 21
3 The RN/CFT Correspondence 23
3.1 Uplifted RN Black Hole . . . . . . . . . . . . . . .23
3.2 The Central Charge . . . . . . . . . . . . . . . . . 26
3.3 Comparison of CFT and BH Entropies . . . . . . . . . 27
3.4 RN/CFT in AdS2/CFT1Viewpoint . . . . . . . . . . . . 28
3.4.1 2D effective action . . . . . . . . . . . . . . . .28
3.4.2 The solutions . . . . . . . . . . . . . . . . . . .29
3.4.3 The boundary counterterms . . . . . . . . . . . . .29
3.4.4 Asymptotic symmetries and central charge . . . . . 30
3.5 Hidden Conformal Symmetry and Conformal Weight . . . 31
3.5.1 Hidden conformal symmetry . . . . . . . . . . . . .31
3.5.2 Absorption cross section . . . . . . . . . . . . . 33
4 The Duality for Kerr-Newman Black Holes 36
4.1 Dynamics of Charged Scalar Field . . . . . . . . . . 36
4.2 Angular Momentum (J-) Picture . . . . . . . . . . . .38
4.3 Charge (Q-) Picture . . . . . . . . . . . . . . . . .39
4.4 General Linear Combination . . . . . . . . . . . . . 41
5 Conclusions and Future Research 43
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . .43
5.2 Future Research . . . . . . . . . . . . . . . . . . .44
Bibliography 46
A Conformal Field Theory 49
A.1 Symmetries and Correlation Functions . . . . . . . . 49
A.2 Examples for 2D CFT . . . . . . . . . . . . . . . . .51
A.2.1 The Free Boson . . . . . . . . . . . . . . . . . . 51
A.2.2 The Free Fermion . . . . . . . . . . . . . . . . . 52
A.3 Central Charge and Virasoro Algebra . . . . . . . . .54
B Symmetry and Casimir Operator of AdS3 58
C Dimensional Reduction 60
C.1 EM field . . . . . . . . . . . . . . . . . . . . . . 61
C.2 Scalar Curvature . . . . . . . . . . . . . . . . . . 61
D Kerr-Newman in AdS2/CFT1Viewpoint 65
D.1 Boundary counterterms . . . . . . . . . . . . . . . .68
D.2 Asymptotic symmetries . . . . . . . . . . . . . . . .69
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指導教授 陳江梅(Chiang-Mei Chen) 審核日期 2012-6-18
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