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研究生： 葉弘裕
Yeh, Hung-yu
論文名稱： Kerr 黑洞中的準正則模
Quasi-Normal Modes of Kerr Black Holes
指導教授： 高賢忠
Kao, Hsien-Chung
學位類別： 碩士
Master
系所名稱： 物理學系
Department of Physics
論文出版年： 2008
畢業學年度： 96
語文別： 英文
論文頁數： 61
中文關鍵詞： 黑洞 、準正則模 、一階修正 、量子重力
英文關鍵詞： Black Holes, Quasi-normal Modes, First-order Corrections, Quantum Gravity
論文種類： 學術論文
相關次數： 點閱：148  下載：17 
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    • 我們利用Teukolsky's radial方程式的解，在複數平面沿著兩條同屬於相同同倫類的路徑做解析連續，其波函數的monodromy必須是相同的，藉此得到Kerr黑洞中的準正則模，而且我們的結果和利用WKB方法所得到的是一致的。我們更進一步討論藉著展開零階的波方程，去計算4維Kerr黑洞準正則模漸進行為的系統性方法。

    We analytically derive quasi-normal frequencies for Kerr black hole by analytically continuing the relevant solution of Teukolsky's radial equation to the complex plane, matching the monodromy of the wave function along two different contours in the same homotopy class. Our results are in agreement with the results from WKB. We also discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies of four-dimensional Kerr black hole by expanding around the zeroth-order approximation to the wave equation.

    Table of Contents iii Abstract v Acknowledgements vi Introduction 1 1 Quasi-Normal Modes of Schwarzschild Black Holes 4 1.1 Linearized field equation . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Regge-Wheeler axial perturbation . . . . . . . . . . . . . . . . . . . . 6 1.3 Linearized equations for axial perturbations . . . . . . . . . . . . . . 10 1.4 Quasi-normal modes in the Laplacian transform . . . . . . . . . . . . 11 1.5 The area spectrum and black hole entropy . . . . . . . . . . . . . . . 16 1.6 Numerical method of quasi-normal frequencies . . . . . . . . . . . . . 18 2 Asymptotic Black Hole Quasi-Normal Frequencies 23 2.1 The Monodromy Theorem . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Quasi-normal frequencies for Schwarzchild black holes . . . . . . . . . 25 2.3 Quasi-normal frequencies for Reissner-Nordstrøm black holes . . . . . 30 2.4 Perturbative calculation of quasi-normal modes of Schwarzchild black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3 Analytic Study of Kerr Black Holes 37 3.1 Teukolsky’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Analysis of quasi-normal modes . . . . . . . . . . . . . . . . . . . . . 39 3.3 Perturbative calculation of quasi-normal modes . . . . . . . . . . . . 44 3.4 Quasi-normal frequencies . . . . . . . . . . . . . . . . . . . . . . . . . 48 4 Conclusion 53 Bibliography 54

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