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系統識別號 U0002-2706201816452100
中文論文名稱 旋轉時空下電磁場的Debye potentials
英文論文名稱 Debye potentials for Electromagnetic Fields in Kerr Spacetime
校院名稱 淡江大學
系所名稱(中) 物理學系碩士班
系所名稱(英) Department of Physics
學年度 106
學期 2
出版年 107
研究生中文姓名 劉欣峴
研究生英文姓名 Xin-Xian Liu
學號 604210079
學位類別 碩士
語文別 英文
口試日期 2018-06-26
論文頁數 29頁
口試委員 指導教授-曹慶堂
委員-劉國欽
委員-陳江梅
中文關鍵字 Debye potential  Principle conformal Killing-Yano tensor  馬克斯威方程組  微分形式  Newman-Penrose形式  canonical basis  Petrov type-D  Kerr-NUT-AdS時空 
英文關鍵字 Debye potential  principal conformal Killing-Yano tenso  Maxwell equations  differential forms  canonical basis  Petrov type-D  Kerr-NUT-AdS metric 
學科別分類 學科別自然科學物理
中文摘要 在這篇論文裡我們利用微分形式引進principal conformal Killing–Yano tensor (PCKYT)並用於解決旋轉時空下的電磁場問題。我們依據Hertz和Debye potential的形式提出利用PCKYT 和Debyepotential得到在四維Kerr-NUT-Ads時空下Hertz potential的假設。最後我們可以得出此假設下的Debyepotential與Newman-Penrose形式中的φ1類似。
英文摘要 In this thesis we introducce the principal Killing-Yano tensor (PCKYT) using differential forms to solve for the electromagnetic fields in curved spacetime. We take the ansatz in which the PCKYT is related to the Hertz and the Debye potential in the 4-dimensional Kerr-NUT-AdS metric. According to the ansatz, we find that the Debye potential is the same as the potential φ1 in the Newman-Penrose formalism.
論文目次 1 Introduction...1
2 Differential forms and Killing-Yano equations...3
2.1 De finition and properties of differential forms...3
2.2 Killing and Killing-Yano equations in terms of differential forms...4
2.3 Principal conformal Killing-Yano tensors and Canonical basis of Kerr spacetime...6
3 Debye Potential from Killing-Yano forms...8
3.1 Debye potential in Minkowski spacetime...8
3.2 Debye potential of PCKYT in Kerr spacetime...9
4 Comparison to the Teukolsky equation...14
4.1 Teukolsky equation and decoupled equation...14
4.2 From the Debye potential equation to a separable equation...16
5 Discussion...19
A Appendix...21
A.1 KT associated with KYT and parallel propagation of KYT...21
A.2 Generalized PCKYT...21
A.3 Harmonic operator on Hertz potential in terms of differential forms...23
A.4 Ricci 2-form...24
A.5 Identity in the NP formalism...26
Bibliography...28
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[17] Misao Sasaki and Takashi Nakamura, Gravitational Radiation From a Kerr Black Hole. 1. Formulation and a Method for Numerical Analysis, Prog. Theor. Phys.67, 1788-1809 (1982).
[18] Scott A. Hughes, Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation, Phys. Rev. D62:044029 (2000); Erratum-ibid. D67:089902 (2003).
[19] Robert M. Wald, Construction of Solutions of Gravitational, Electromagnetic, or Other Perturbation Equations from Solutions of Decoupled Equations, Phys. Rev. Lett.41, 203-206 (1978).
[20] Oleg Lunin, Maxwell's Equations in the Myers-Perry Geometry, Ph.D. thesis, University of Albany(SUNY), Albany, NY 12222, USA (2017).
[21] Pavel Krtous, Valeri P. Frolov, and David Kubiznak, Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes, JHEP (2018).
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