SL(4,R)理論下的漸近平直對稱轉換

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龔大勝(Da-Sheng Kung) 查詢紙本館藏

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物理學系

論文名稱

SL(4,R)理論下的漸近平直對稱轉換
(Asymptotic Flatness Preserving Transformations in SL(4,R) sigma-model)

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摘要(中)

考慮一個具有SL(4,R)對稱性的五維理論，其中包含重力場、一個純量場及一個三階向量場，我們提出保持時空漸近平直的對稱轉換所必須滿足的條件，統整出在不同座標描述的平直時空中，滿足該條件的所有轉換。這篇論文主要針對以下三種不同時空結構做討論：Kaluza-Klein黑洞、五維的黑洞和black ring，我們詳細列出所有滿足漸近平直條件的對稱轉換，並且討論這些轉換所代表的物理意義，其中部分轉換可以給出帶有電荷的解。

摘要(英)

We give a systematic method to determine the asymptotic flatness preserving transformations
in the three-dimensional SL(4,R)/SO(2, 2) sigma-model arising from a
five-dimensional gravity coupled to a dilaton and a three-form field. The permitted
transformations depend on the coordinate choices. By focusing on three cases,
namely the Kaluza-Klein black hole, five-dimensional black hole and black ring, we
find out all possible asymptotic flatness preserving transformations and apply them
to generate charge from single rotating vacuum solutions.

關鍵字(中)

★ 漸近平直
★ SL(4
★ R)模型
★ 五維黑洞

關鍵字(英)

★ asymptotic flat
★ SL(4
★ R) sigma-model
★ five dimensional black hole
★ black ring

論文目次

1 Introduction 1
2 SL(4,R) Symmetry 4
2.1 Sigma-model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Basic symmetry transformations . . . . . . . . . . . . . . . . . . . . . 7
2.3 Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Asymptotic Flatness Preserving 13
3.1 AFP condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Kaluza-Klein vacuum R3,1 × S1 . . . . . . . . . . . . . . . . . . . . . 15
3.3 5D Minkowski R4,1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Ring coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Charged Kaluza-Klein Black Holes 21
4.1 R1 − L1 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 T2 + T3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 R2 + L3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4 S2 + S3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.5 R3 + L2 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.6 R4 − L4 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Charged 5D Black Holes 26
5.1 S3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2 R2 + L3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2.1 Physical quantity . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.2 An equivalent approach . . . . . . . . . . . . . . . . . . . . . 29
6 Charged Ring Solutions 31
6.1 Neutral black rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 S3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.3 R2 + L3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.3.1 Physical quantity . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.3.2 An equivalent approach . . . . . . . . . . . . . . . . . . . . . 37
7 Conclusion 39
7.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Bibliography 41
A Kaluza-Klein theory 43
B Relations of gauge field components 45
C Black Rings 46
C.1 Ring coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
C.2 Neutral black rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
D Target-space potentials 52

參考文獻

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指導教授

陳江梅(Chiang-Mei Chen)

審核日期

2008-5-23

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