博碩士論文 952202010 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:6 、訪客IP:3.230.154.129
姓名 楊寶鴻(Poh-Hoong Yong)  查詢紙本館藏   畢業系所 物理學系
論文名稱 在Kerr幾何的特殊正交座標系和狄拉克旋子
(Special orthonormal frames and Dirac spinors in Kerr geometry)
相關論文
★ Kerr-Sen 時空的準局域能量與角動量★ Brill 波時空於特殊正交坐標系的初值問題之數值解
★ Teleparallel重力理論中的準局域能量、動量和角動量★ 度規仿射重力理論中的準局域能量-動量
★ 廣義相對論理論中之準局域質心距★ 幾何代數與微分形式間之轉換及其在重力之應用
★ 幾何代數下的旋量與重力場正能量★ 幾何代數與Clifforms之轉換及其於重力哈密頓函數與準局域量之應用
★ Teleparallel 理論中之準局域質心距★ 廣義相對論的準局域量的小球極限
★ 重力場中準局域角動量的旋子表述★ 有Torsion效應的宇宙
★ 準區域的膺張量和陳聶式子★ 準局部能量與參考系之選擇
★ 球對稱時空的準局域能量★ Poincaré Gauge Theory with Coupled Even and Odd Parity Spin-0 Dynamic Connection Modes: Isotropic Bianchi Cosmologies
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 愛因斯坦的廣義相對論是一個與座標選取無關的理論,所以我們有選取座標系的自由度。我運用聶斯特教授發展出來的規範條件來選取一個正交歸一的座標,並運用在Reissner-Nordstrom 和 Kerr 幾何時空上面。這個規範條件選擇了一個特定的標架。這種特定的標架在重力系統的正能量定理証明上特別有用。另外,這種特定的標架和狄拉克方程試息息相關,透過解狄拉克方程,我們就可以選出特定的標架滿足規範條件。然而,在彎曲的時空中,要解出狄拉克方程不是一件簡單的事。我們考慮了弱重力場條件下如何定義特定的標架,還有在Reissner-Nordstrom 和 Kerr 時空上求出狄拉克方程漸近常數的解。
摘要(英) Since Einstein’’s gravity theory is a frame independent theory, we have the freedom of choosing an orthonormal frame. I use Nester’’s gauge condition to select a preferred orthonormal frame for some gravitational systems including the Reissner-Nordstrom and Kerr geometry. The gauge condition selects a special orthonormal frame (SOF). A SOF has application in particular to a positive energy proof and energy localization for a gravitational system. This gauge condition is related to the solution of the Dirac equation; by solving the Dirac equation we can determine a special orthonormal frame. However, in curved spacetime the solution of Dirac equation is highly nontrivial. We calculated the weak field limit case and
found the asymptotically constant solution for the Dirac equation in the Reissner-Nordstrom and Kerr geometry.
關鍵字(中) ★ 狄拉克
★ 旋子
★ 座標系
關鍵字(英) ★ Dirac spinor
★ orthonormal frame
★ Kerr geometry
論文目次 1 Introduction 1
2 Special orthonormal frames 4
2.1 Orthonormal tetrads. . . . . . . . . . . . . . . . 4
2.2 Special orthonormal frames . . . . . . . . . . . . 5
2.3 Isotropic metric . . . . . . . . . . . . . . . . . 10
3 SOF in Reissner-Nordstrom geometry 12
3.1 Isotropic form of Reissner-Nordstrom . . . . . . . 12
3.2 Three-dimensional R-N solution. . . . . . . . . . . 14
4 Dirac spinor in Kerr geometry 23
4.1 Weak field approximation of the Kerr solution. . . . 24
4.2 Newman-Penrosre formalisms . . . . . . . . . . . . 26
4.3 Dirac equation in Kerr geometry . . . . .. . . . . . 27
4.3.1 Minkowski . . . . . . . . . . . . . . . . . . . . 31
4.3.2 Schwarzschild . . . . . . . . . . . . . . . . . . 32
4.3.4 Kerr . . . . . . . . . . . . . . . . . . . . . . .34
4.3.4 Frobenius method. . . . . . . . . . . . . . . . . 36
4.4 Scalar and psuedoscalar . . . . .. . . . . . . . .. 42
5 Conclusion 44
Bibliography . . . . . . . . . . . . . . . . . . . . 46
參考文獻 [1] J. M. Nester, A gauge condition for orthonormal three-frames, J. Math. Phys 30, 624 (1989).
[2] J. M. Nester, A positive gravitational energy proof ,
Phys. Lett. A 139, 112 (1989).
[3] J. M. Nester,Positive energy via teleparallel Hamiltonian , Int. J. Mod. Phys. A 4, 1755 (1989).
[4] J. M. Nester, Special orthonormal frames and energy localization, Class. Quantum Grav. 8, L19 (1991).
[5] J. M. Nester, Special orthonormal frames, J. Math. Phys 33, 910 (1992).
[6] J. M. Nester and R. S. Tung, Another positivity proof and gravitational energy localizations , Phys. Rev. D 49, 3958 (1994).
[7] J. M. Nester, R. S. Tung and Y. Z. Zhang, Ashtekar's new variable and positive energy ,
Class. Quantum Grav. 11, 757 (1994).
[8] J. M. Nester, R. S. Tung and V. V. Zhytnikov, Some spinor-curvature identies ,
Class. Quantum Grav. 11, 983 (1994).
[9] J. M. Nester, A new gravitational energy expression with a simple positivity proof, Phys. Lett. A 83A, 241 (1981).
[10] E. Israel and J. M. Nester, Positivity of the Bondi gravitational mass, Phys. Lett. A 85A, 259 (1981).
[11] J. N. Nester, The Gravitational Hamiltonian, Asymptotic Behavior of Mass and Space-Time Geometry (Lecture Notes in Physics vol 202) , pp 155-63, edited F. Flaherty (Berlin, Springer 1984)
[12] J. Isenberg and J. Nester, Canonical Gravity, in General Relativity and Gravitation. One Hundred Years the Birth of Albert Einstein, Vol. 1, pp 23-97, edited A. Held (Plenum Press, NewYork, 1980).
[13] A. Dimakis and F. Muller-Hoissen, On a gauge condition for orthonormal three-frames, Phys. Lett. A 142, 73 (1989).
[14] A. Dimakis and F. Muller-Hoissen, Spinor field and the positivity energy theorem, Class. Quantum Grav. 7, 283 (1990).
[15] R. Schoen and S.T. Yau, On the positive mass conjecture in general relativity, Commun. Math. Phys. 65, 45 (1979).
[16] E. Witten, A new proof of the positive energy theorem, Commun. Math. Phys. 80, 381 (1981).
[17] S. Chandrasekhar, Solution of Dirac's equation in Kerr geometry, Proc. R. Soc. Lond. A 349, 571 (1976).
[18] S. Chandrasekhar, On Mass-Dependent Spheroidal Harmonics of Spin One-Half, Proc. R. Soc. Lond. A, 391, 27 (1984).
[19] S. Chandrasekhar, The Mathematical Theory of Black Holes Oxford University Press, UK, (1983)
[20] S. A. Teukolsky, Perturbations of a rotating black hole I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations, Astrophys. J.185}, 635
(1973).
[21] J. B. Hartle and D. C. Wilkins, Analytic Properties of the Teukolsky Equation, Phys. Lett. A 203, 5-11 (1995).
[22] D. Ranganathan, Exact solutions to the Chandrasekhar Page angular equation, (2006), arXiv:gr-qc/0601057v2.
[23] R. H. Good, Jr. , Preperties of the Dirac Matrices
, Rev. Mod. Phys. extbf{27}, 187 (1955).
[24] W. T. Payne, Elementary Spinor Theory, Am. J. Phys. 20, 253 (1952).
[25] D. R. Brill and J. A. Wheeler , Interaction of Neutrinos and Gravitational Fields, Rev. Mod. Phys. 29, 465 (1957).
[26] L. B. Szabados, Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article, Living Rev. Relativity 7, (2004), 4. http://www.livingreviews.org/lrr-2004-4.
[27] R. Penrose and W. Rindler, Spinors and space-time, Vol. 1: Two-Spinor Calculus and Relativistic Fields,
Cambridge University Press, Cambridge, (1984).
[28] R. Penrose and W. Rindler, Spinors and space-time, Vol. 2: Spinor and Twistor Methods in Space-Time Geometry , Cambridge University Press, Cambridge, (1986).
[29] P. Lounesto, Clifford Algebras and Spinors, 2nd edition, Cambridge University Press, Cambridge, (2001)
[30] C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman, New York, (1973)
[31] H. Flanders, Differential Forms with
Applications to the Physical Sciences Dover, New York, (1989).
[32] J. M. Nester, On the zeros of spinor fields and
an orthonormal frame gauge condition, to be appear in Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, World Scientific, (2007).
指導教授 聶斯特(James M. Nester) 審核日期 2008-7-6
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明