Schwinger Effect in Near Extremal Charged Black Holes

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姓名

唐富一(Fu-Yi Tang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Schwinger Effect in Near Extremal Charged Black Holes)

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摘要(中)

我們在靠近視界且近極端帶電黑洞的時空下研究粒子的成對產生，由於背景電磁場以及視界的緣故，成對產生的機制有施溫格效應以及霍金輻射。首先我們研究了近視界幾何的全像對偶，其中 Reissner-Nordstr"om 黑洞的近視界幾何是 AdS$_2$ $ imes$ S$^2$，而 Kerr-Newman 黑洞的近視界幾何是 warped-AdS$_3$。
根據AdS/CFT對偶，我們可以找到相對應的二維共形場論描述，而且每個帶電黑洞的守恆量(除了質量)會有相對應的共形場論圖像。
我們也檢驗了在低能量探測場的情況下的非極端黑洞的全像描述。
對於近極端帶電黑洞時空下的成對產生，在設定了邊界條件之後，我們對於純量場和旋量場分別計算了平均產生數，真空維持量以及吸收截面。特別的是，平均產生數有熱力學解釋而且可以用哈密頓-雅可比方法來獲得同樣的結果，
其中平均產生數可以分成兩個部分來表示，一個是 AdS 時空下的施溫格效應，而另一個是 Rindler 時空下的施溫格效應。而且平均產生數和吸收截面也有二維共形場論描述。

摘要(英)

We investigate the spontaneous pair productions in the near horizon regions of
near extremal charged black holes,
and the corresponding mechanisms are Schwinger effect and Hawking radiation
due to the external electromagnetic fields and causal boundaries.
Firstly, we study the holographic dualities
for the near horizon geometries, which are
AdS$_2$ $ imes$ S$^2$ for Reissner-Nordstr"om (RN) black hole and warped-AdS$_3=$ AdS$_2$ $ imes$ S$^1$ for Kerr-Newman (KN) black hole.
According to AdS/CFT correspondence,
there are corresponding dual $2$-dimensional conformal field theory (CFT$_2$) descriptions,
and will display individual pictures associated with the "hairs" (besides mass) carried by the charged black holes.
The holographic dualities for non-extremal black hole
are also investigated in low frequencies of the probe field.
For pair productions in the near extremal charged black holes, we
calculate the
physical quantities, i.e.,
mean number of production, vacuum persistence amplitude,
and absorption cross section, for both scalar and spinor cases
after imposing the outer boundary condition.
In particular, the mean number of production
has thermal interpretations and can be evaluated by the Hamilton-Jacobi approaches,
in which the contributions of production rate can
be expressed in two parts, one is Schwinger effect in the AdS space,
and the other is the same effect in the Rindler space.
Moreover, the production rate and the absorption cross section also have dual CFT$_2$ descriptions based on the holographic dualities of charged black holes.

關鍵字(中)

★ 黑洞
★ AdS/CFT對偶
★ 施溫格效應

關鍵字(英)

★ Black Hole
★ AdS/CFT duality
★ Schwinger Effect

論文目次

1 Introduction 1
I Holographic Descriptions 7
2 Reissner-Nordstr¨om/CFT 8
2.1 Background Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Warped-AdS 3 /CFT 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Uplifted to 5D . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Central Charges . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 AdS 2 /CFT 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Hidden Conformal Symmetries . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Greybody Factor . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Electromagnetic Duality . . . . . . . . . . . . . . . . . . . . . 21
3 Kerr-Newman/CFT 23
3.1 Background Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Warped-AdS 3 /CFT 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Uplifted to 5D . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.3 Central Charges . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Hidden Conformal Symmetries . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Greybody Factor . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 General Pictures . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Monodromy Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 33
II Schwinger Eﬀect 39
4 Scalar Particle Creation in RN Black Hole 40
4.1 Particle Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Scalar Particle Creation . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Extremal RN Black Hole . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 Near Extremal RN Black Hole . . . . . . . . . . . . . . . . . . . . . . 45
4.6 Dyonic Particle Creation . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Dual CFT Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5 Spinor Particle Creation in RN Black Hole 50
5.1 Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Spherical Spinor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.3 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4 Asymptotic and Near Horizon Behaviors . . . . . . . . . . . . . . . . 53
5.5 Spinor Particle Creation . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.6 Dual CFT Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Scalar Particle Creation in KN Black Hole 58
6.1 Scalar Particle Creation . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Dyonic Particle Creation . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.3 Dual CFT Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.4 Thermal Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7 Spinor Particle Creation in KN Black Hole 68
7.1 Newman-Penrose Formalism . . . . . . . . . . . . . . . . . . . . . . . 68
7.2 Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.3 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.4 Dual CFT Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8 Conclusion 74
Bibliography 76
A Special Functions 82
A.1 Wittaker Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
A.2 Hypergeometric Functions . . . . . . . . . . . . . . . . . . . . . . . . 82
B Surface Charge 84
C Rindler Space 87
D 2-dimensional CFT 89
E Dirac Equation in NP Formalism 95

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指導教授

陳江梅(Chiang-Mei Chen)

審核日期

2017-7-27

推文