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研究生： 張永輝
Chang, Yung-Hui
論文名稱： 內蘊時間重力與封閉羅伯遜-沃爾克時空之重力波
Intrinsic Time Gravity and gravitational waves in closed Robertson-Walker spacetimes
指導教授： 許祖斌
Soo, Cho-Pin
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： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 45
中文關鍵詞： 內蘊時間重力 、重力波 、封閉羅伯遜-沃爾克時空 、連帶的勒壤得多項式
外文關鍵詞： Intrinsic Time Gravity, gravitational waves, closed Roberson-Walker spacetimes, associated Legendre polynomials
相關次數： 點閱：156  下載：14 
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    • 此論文於內蘊時間重力架構下探討封閉羅伯遜沃爾克時空中的重力波。內蘊時間重力以空間體積變化幅度作為內蘊時間來描述重力物理的哈密頓演化。重力波方程由純愛因斯坦廣義相對論或額外添加一項Cotton-York的哈密頓量中導出。含物理意義的微擾態可用封閉羅伯遜沃爾克時空的空間球諧張量展開，而態的時間相關解則是與連帶的勒壤得多項式（associated Legendre polynomials）有關。文中也探討了早期和晚期宇宙有無Cotton-York項貢獻的差別，也顯示出了其貢獻有別於單純愛因斯坦理論的特徵。

    This work investigates gravitational waves in closed Roberson-Walker spacetimes in the context of Intrinsic Time Gravity which describes the Hamiltonian evolution of gravitational physics in which the fractional change of the spatial volume is used as the intrinsic time variable. Gravitational wave equation is derived, and solved for Einstein’s theory as well as for General Relativity modified by an extra Cotton-York term in the Hamiltonian. Physical transverse traceless gravitational modes are expanded in terms of spherical harmonics of spatially closed Robertson-Walker spacetimes; time-dependence of the modes are solved exactly and are found to be related to associated Legendre polynomials. Different domains corresponding to early and late times with and without Cotton-York contribution are studied and the behavior of the modes are revealed. A salient feature of Cotton-York contribution which distinguishes it from pure Einstein theory is pointed out.

    摘要i Abstract ii 誌謝iii Table of Contents iv List of Figures v Chapter 1. Introduction and overview 1 Chapter 2. Intrinsic Time Gravity and Hamilton’s equations for spatial metric evolution 3 Chapter 3. Gravitation waves in closed Robertson–Walker spacetimes 5 Chapter 4. Solving the time dependence of the modes 14 Chapter 5. Associated Legendre polynomials and their application 16 Chapter 6. Gravitational waves in Einstein’s theory and in the CottonYork era 25 ζ → 0 . . . . . . . . . . . . . . . 25 Large ζ . . . . . . . . . . . . . . . . . . . . 28 . k large enough and x is not very large . . . . . . . . . . . . . . . . . . 28 . k and x both large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 ζ not extremely small and x is small . . . . . . . . . . . . . . . . . . . . . . . 31 Chapter 7. Conclusions and further remarks 33 References 35 Appendix A. 36

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    [3] For observational evidence of our compact universe, see, for instance, E. Di Valentino, A. Melchiorri and J. Silk, Nat. Astron. 4 (2020) 196.
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    [8] N. O. Virchenko and I. Fedotova Generalized associated Legendre functions and their applications (World Scientific , 2001).
    [9] J.R. Klauder, Int. J. Geom. Methods Mod. Phys. 3 (2006) 81

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