博碩士論文 93222018 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:5 、訪客IP:3.227.2.246
姓名 劉建良(Jian-Liang Liu)  查詢紙本館藏   畢業系所 物理學系
論文名稱 準局部能量與參考系之選擇
(On quasi-local energy and the choice of reference)
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★ 在Kerr幾何的特殊正交座標系和狄拉克旋子
★ 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) 根據協變哈密頓方法,我們可以決定引力系統的準局部量。有幾個相依於邊界條件的邊界項是可行的,但其中有一個 (與協變Dirichlet邊界條件相關)有最佳的性質;它給出ADM能量、Bondi能量及能流的正定性。此表示式一如其他表示式一樣也依賴於參考系及位移向量的選擇。如何做出最佳的選擇至今仍不清楚。本文計算幾個例子,包括FRW宇宙、第五類Bianchi模型、及Schwarzschild幾何在三種不同座標系的情形。計算結果顯示:準局部能量並不是唯一決定的,甚至於閔氏時空也能得到非零解。此結果是因為選擇不同參考系的緣故,而對於平直時空,度規張量仍有任意的選擇方式。我們藉由對準局部能量取極值的方式,找到一種決定參考系及位移向量的條件,使能量的表示式只依賴於物理系統,然而參考系的選擇仍有一定的任意性。此能量表示式在Schwarzschild幾何的三個不同形式下皆得到相同的值。
摘要(英) Using the covariant Hamiltonian approach, we can determine the quasi-local quantities for a gravitating system within a region from an integral over its two-boundary. There are several possible boundary terms associated with different boundary conditions, but there is one (which corresponds to a kind of covariant Dirichlet condition on the metric) which has the best properties; it gives the ADM and Bondi energy and energy flux as well as having a positivity property. Like others this expression depends on the choice of reference configuration and the displacement vector field. It is not yet clear how to best make these choices. Here we calculate several cases including the FRW cosmologies, the Bianchi V model, and the Schwarzschild geometry in three different coordinate systems. The results imply that the quasi-local energy is not uniquely determined, even in Minkowski space one could also get a nonvanishing value. This result comes from the different choices of the reference frame. There is an arbitrary choice for the reference of flat space. By extremizing the quasi-local energy, we found a strategy to choose both the reference and the displacement vector to get the same energy value in the three Schwarzschild geometry cases. Although there are still many choices, it is not quite arbitrary anymore.
關鍵字(中) ★ 哈密頓
★ 邊界項
★ 準局部能量
★ 參考系
★ 位移向量
關鍵字(英) ★ displacement vector
★ Hamiltonian
★ reference
★ boundary term
★ quasi-local energy
論文目次 1 Introduction 1
2 Background 4
2.1 First-order Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Hamiltonian formulation . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Application to general relativity . . . . . . . . . . . . . . . . . . . . . 10
3 Calcuations 13
3.1 FRW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Bianchi V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Schwarzschild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 Eddington-Finkelstein . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 Painlev′e-Gullstrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6 Extremize the energy to restrict the reference . . . . . . . . . . . . . 29
3.6.1 FRW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6.2 Schwarzschild . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.6.3 Eddington-Finkelstein . . . . . . . . . . . . . . . . . . . . . . 34
3.6.4 Painlev′e-Gullstrand . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Conclusion 36
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
A Variation of Einstein-Hilbert action 42
B Mean curvature 45
B.1 FRW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
B.2 Bianchi V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
B.3 Schwarzschild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
B.4 Eddington-Finkelstein . . . . . . . . . . . . . . . . . . . . . . . . . . 49
B.5 Painlev′e-Gullstrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
C Different reference frames 51
C.1 Schwarzschild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
C.2 Eddington-Finkelstein . . . . . . . . . . . . . . . . . . . . . . . . . . 55
C.3 Painlev′e-Gullstrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
C.4 Another choice of reference frames . . . . . . . . . . . . . . . . . . . . 60
C.4.1 Schwarzschild . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
C.4.2 Eddington-Finkelstein . . . . . . . . . . . . . . . . . . . . . . 63
C.4.3 Painlev′e-Gullstrand . . . . . . . . . . . . . . . . . . . . . . . . 65
參考文獻 [1] C.M. Chen, J. M. Nester and R. S. Tung, “Hamiltonian boundary term and quasilocal energy flux”, Phys. Rev. D 72, 104020 (2005).
[2] C. M. Chen, J. M. Nester, and R. S. Tung, “Quasilocal energy-momentum for geometric gravity theories”, Phys. Lett. A 203, 5-11 (1995).
[3] C. M. Chen and J. M. Nester, “Quasilocal quantities for GR and other gravity theories” , Class. Quantum Grav. 16, 1279-1304 (1999).
[4] C.M. Chen and J.M. Nester, “A Symplectic Hamiltonian Derivation of Quasilocal Energy-Momentum for GR”, Gravitation Cosmol. 6, 257 (2000).
[5] 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.
[6] T. Regge and C. Teitelboim, “Quasilocal energy and conserved charges derived from the gravitational action”, Phys. Rev. D47, 1407 (1993).
[7] R. Beig and N. ′O Murchadha, “The Poincar′e Group as the Symmetry Group of Canonical General Relativity”, Ann. Phys. (N.Y.) 174, 463-498 (1987).
[8] N. ′O Murchadha, L. Szabados, and P. Tod, “Positivity of Quasilocal Mass ”, Phys. Rev. Lett. 92, 259001 (2004).
[9] M. Liu and S.T. Yau, “Positivity of Quasilocal Mass”, Phys. Rev. Lett. 90, 231102 (2003).
[10] M. Liu and S.T. Yau, “Positivity of quasi-local mass II ”, J. Amer. Math. Soc. 19, no.1, 181-204 (2006), arXiv:math.DG/0412292.
[11] J. D. Brown and J. W. York, “Quasilocal energy and conserved charges derived
from the gravitational action”, Phys. Rev. D 47, 1407-1419 (1993).
[12] K. Kuchaˇr, “Dynamics of tensor fields in hyperspace. III ”, J. Math. Phys. (N.Y.) 17, 801 (1976).
[13] L. B. Szabados, “On the roots of the Poincar′e structure of asymptotically flat spacetimes”, Classical Quantum Gravity 20, 2627 (2003).
[14] R. Sachs, “Gravitational Waves in General Relativity. VIII. Waves in Asymptotically Flat Space-Time”, Proc. R. Soc. A 270, 103 (1962).
[15] H. Bondi, M. G. J. van der Berg, and A. W. K. Metzner, “Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems”, Proc.
R. Soc. A 269, 21 (1962).
[16] J. M. Nester, “General pseudotensors and quasilocal quantities”, Classical Quantum Gravity 21, S261 (2004).
[17] J. M. Nester, “A manifestly covariant Hamiltonian formalism for dynamical geometry”, Tainan school on Cosmology and Gravitation, 2007/01/14.
[18] T. Regge and C. Teitelboim, “Role of Surface Integrals in the Hamiltonian Formulation of General Relativity”, Ann. Phys. (N.Y.) 88, 286 (1974).
[19] C.W. Misner, K.S. Thorne and J.A. Wheeler, “Gravitation” (Freeman, New York, 1973)
[20] Liang Canbin, Zhou Bin, “Weifenjihe Rumen Yu Guangyixiangduilum” (Beijin Normal University, 2006).
[21] Ray D’Inverno, “Introducing Einstein’s Relativity” (Oxford: New York, Toronto, 1993).
[22] R.M. Wald, “General Relativity” (The University of Chicago Press, 1984).
[23] Edit by J. M. Nester, C. M. Chen, and J. P. Hsu “Gravitation and Astrophysics” (World Scientific 2007).
[24] C. M. Chen, “Quasilocal Quantities for Gravity Theories”, MSc. Thesis, (National Central University) unpublished (1994).
[25] C. C. Chang, “The Localization of Gravitational Energy: Pseudotensors and Quasilocal Expressions”, MSc. Thesis, (National Central University) unpublished (1999).
[26] J. E. Lidsey, D. Wands, E. J. Copeland, “Superstring Cosmology”, Phys. Rept. 337 343-492 (2000), arXiv:hep-th/9909061v2.
[27] L. B. Szabados, “Two dimensional Sen connections in general relativity”, Class. Quant. Grav. 11, 1833-1846 (1994).
[28] R. Penrose, “Quasi-Local Mass and Angular Momentum in General Relativity”, Proc. R. Soc. London A381, 53-63 (1982).
指導教授 聶斯特(James M. Nester) 審核日期 2007-7-19
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