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研究生： 蔡明政
Ming-Jang Tasi
論文名稱： 克爾-紐曼黑洞下的成對產生
Spontaneous Pair Production in Kerr-Newman Black Holes
指導教授： 陳江梅
Chiang-Mei Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2015
畢業學年度： 103
語文別： 英文
論文頁數： 43
中文關鍵詞： 克爾-紐曼黑洞下的成對產生 、彎曲時空中的量子場論
外文關鍵詞： Spontaneous Pair Production in Kerr-Newman Black Holes, Quantum Field in Curved Spacetime, Particle Creation by Gravitational Fields, Near Horizon Near Extremal Limit
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    • 本篇論文主要是研究帶電跟角動量的時空背景下也就是KN黑洞 粒子成對產生發射到無窮遠處
    首先透過量子場論在彎曲空間下討論真空中粒子如何產生
    在彎曲空間中有Bogoliubov關係式連結時空中不同兩點的狀態 係數B並不消逝而有粒子產生
    然後透過計算通量的方式
    告訴帶電純量場在這樣的幾何下如何產生並發射出來
    取近極端近事件視界極限
    我們可以得到近極端近事件視界的KN黑洞的幾何
    由通量守恆可以得到一個類比於Bogoliubov關係式的式子 其中B跟beta在粒子生成扮演重要角色
    分別考慮極端KN黑洞 和 近極端KN黑洞 計算粒子在視界附近穿隧出來射向無窮遠的通量

    In this thesis we mainly study the production of pair particles carrying energy, electricity and angular momentum of the background, which is a Kerr-Newman (KN) black hole. Firstly we review the quantum field theory in curved spacetime to discuss the vacuum particle production by connecting quantum field at two different points in spacetime via the Bogoliubov relation. More precisely, the non-vanishing $B$ coefficients indicates the appearance of the particle production.

    We then analysis the charged scalar production appearing at the near-horizon region of near-extremal KN black hole via the ratios of the fluxes of in- and out-going propagating modes at two boundaries. From the conservation of flux one can obtain a expressions analogy to the Bogoliubov relation. Thus the Bogoliubov coefficients, consequently the essential physical quantities, such as vacuum persistence, mean number of production and absorption cross section, can be obtained.

    1 Introduction 1 2 Quantum Field in Curved Spacetime 3 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Canonical Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 From Hilbert Space to Fock Space . . . . . . . . . . . . . . . . . . . . 6 2.4 Particle Creation by Gravitational Fields . . . . . . . . . . . . . . . . 8 2.4.1 Real scalar eld . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4.2 Complex scalar eld . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Spontaneous Pair Production in Kerr-Newman Black Holes 15 3.1 Kerr-Newman Black Holes . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Near Horizon Near Extremal Limit . . . . . . . . . . . . . . . . . . . 18 3.3 Charged Scalar Field in NHEKN Background . . . . . . . . . . . . . 19 3.4 Pair Production in Extremal KN Black Holes . . . . . . . . . . . . . 21 3.4.1 Outer Boundary Condition . . . . . . . . . . . . . . . . . . . . 23 3.4.2 Inner Boundary Condition . . . . . . . . . . . . . . . . . . . . 24 3.5 Pair Production in Near-Extremal Case . . . . . . . . . . . . . . . . . 25 3.5.1 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . 26 3.6 Pair Production in KN and RN Black Holes . . . . . . . . . . . . . . 27 3.7 Cosmic Censorship Condition . . . . . . . . . . . . . . . . . . . . . . 28 4 Conclusion 30 A Properties of Some Special Functions 32 A.1 Whittaker Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 A.2 Hypergeometric Functions . . . . . . . . . . . . . . . . . . . . . . . . 33 A.3 Gamma Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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