博碩士論文 105222027 詳細資訊




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姓名 魏君宇(Chun-Yu Wei)  查詢紙本館藏   畢業系所 物理學系
論文名稱
(The Echo of Charged Black Holes)
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摘要(中) 在帶有電荷黑洞的背景下,又稱帶電黑洞為萊斯納 (Hans Reissner)- 諾斯壯 (Gunner Nordström) 黑洞 (萊-諾黑洞) ,我們考慮俱有質量與電荷量的測試純量場,被吸入萊- 諾黑洞中。藉由量子力 學理論的概念,測式純量場將激發黑洞,使黑洞發射出訊息。利用克萊恩- 戈登 (Klein- Gordon) 方程式的解析和推算,我們將獲得發射出的訊息,其為一條波動方程式。此波動方程乃為二階常微分 波動方程 (ODE),其形式與匯合式的休恩 (confluent Heun) 微分方程式雷同。但不幸的事,休恩C (HeunC) 微分方程式到目前為止,還沒有精確的解析方程解,因此,我們嘗試找出一組近似波動函數解。假設一組近似波函動數數列,使波動函數數列必須滿足二階常微分波動方程 。利用聲納回傳探測的想法,允許我們考慮無邊界條件下,解析射出的訊息為何,此邊界條件又稱為類駐波邊界 (quasi-normal boundary) 條件。當波動函數滿足波動方程和無邊界條件後,我們將獲得一組三項遞迴關係式。最後,利用類似泰勒展開式的方法,展開和估算遞迴關係式的高階項,並解遞迴關係式的特徵值,則可得到波動方程式的近似波動頻率。
摘要(英) Consider the Klein-Gordon (KG) equation with a massive and charged scalar field in the Reissner- Nordstrom (RN) black hole, we obtain a wave equation which is a second-order ordinary differential equation (ODE). The wave equation is identified with the confluent Heun differential equation which, unfortunately, does not have the exactly solution so far. Hence, here we consider the quasi-normal boundary and present a method which is the three-terms of recurrence relation to approximate the frequency of wave equation.
關鍵字(中) ★ 帶電黑洞
★ 類駐波
關鍵字(英) ★ RN black holes
★ QNM
論文目次 1 Introduction 1
2 Boundary Condition of QNM 3
3 Wave Equation of Scalar Field 6
4 Method of Recurrence Relation 8
5 QNM of Schwarzschild Black Hole 11
6 QNM of RN Black Hole 15
7 Discussion 17
A QNM by Mathematica 18
A.1 Recurrence Relation .................................... 19
A.2 Approximation ....................................... 20
A.3 Frequency of QNM..................................... 20
A.3.1 Continued Fraction................................. 21 A.3.2 Determinant of Matrix............................... 21 A.3.3 Plot of QNM .................................... 21
B QNM by Matlab 22
參考文獻 [1] Juan Carlos Degollado and Carlos A. R. Herdeiro. Stationary scalar configurations around extremal charged black holes. Gen. Rel. Grav., 45:2483–2492, 2013.
[2] Steven Detweiler. On resonant oscillations of a rapidly rotating black hole. Proc. R. Soc. Lond. A, 352(1670):381–395, 1977.
[3] Valeria Ferrari and Bahram Mashhoon. New approach to the quasinormal modes of a black hole. Physical Review D, 30(2):295, 1984.
[4] Shahar Hod. Bohr’s correspondence principle and the area spectrum of quantum black holes. Physical Review Letters, 81(20):4293, 1998.
[5] E. W. Leaver. An Analytic representation for the quasi normal modes of Kerr black holes. Proc. Roy. Soc. Lond., A402:285–298, 1985.
[6] Lubos Motl. An analytical computation of asymptotic schwarzschild quasinormal frequencies. arXiv preprint gr-qc/0212096, 2002.
[7] Hans-Peter Nollert. Quasinormal modes of schwarzschild black holes: The determination of quasinormal frequencies with very large imaginary parts. Physical Review D, 47(12):5253, 1993.
[8] William H. Press. Long Wave Trains of Gravitational Waves from a Vibrating Black Hole. Astrophys. J., 170:L105–L108, 1971.
[9] Tullio Regge and John A Wheeler. Stability of a schwarzschild singularity. Physical Review, 108(4):1063, 1957.
[10] J. Weber. Evidence for discovery of gravitational radiation. Phys. Rev. Lett., 22:1320–1324, 1969.
指導教授 陳江梅(Chiang-Mei Chen) 審核日期 2019-7-4
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