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研究生:孟繁蕃
研究生(外文):Feng-Feng Meng
論文名稱:廣義相對論理論中之準局域質心距
論文名稱(外文):Quasilocal center-of-mass moment in general relativity
指導教授:聶斯特
指導教授(外文):JM Nester
學位類別:碩士
校院名稱:國立中央大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:68
中文關鍵詞:廣義相對論重力場準局域量質心距
外文關鍵詞:general relativityquasilocal quantitycenter-of-mass moment
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既然重力場中不存在能量與動量之密度,則應致力於
尋求各守恆量之準局域量.本文繼同一系列研究之後,探
討在廣義相對論理論中之質心距之準局域量,由此非但可
以再次驗証Nester-Chen expression之有效性,更能顯示
質心距較其他守恆量對各種表示式理論提供更嚴格之檢驗
標準


Having recognized the absence of energy and momentum density for the gravitational field, conserved quasilocal quantities over finite 3- dimensional regions are the best that can be expected. Nester-Chen expression for the quasilocal center-of-mass moment was investigated.
Not only the result agrees with the expectated asymptotical limit value but also the center-of-mass moment behaves as a more strict criteria for the validity of the expression.


Chapter 1. Introduction ......................................1
§1. Outline .................................................1
§2. Mathematical notations ...................................2
§3. Absence of energy and momentum density ..................2
§4. Center-of-mass moment ...................................4
Chapter 2. General Lagrangian formulation ....................7
§1. δL .....................................................7
§2. H= ZμHμ+ dB ...........................................9
§3. Hμ is proportional to variational derivatives ..........10
§4. The role of B ..........................................11
§5. δH ...................................................12
Chapter 3. Lagrangian formulation in GR .....................16
§1. Various theories in relativity .........................16
§2. L EC in GR ..............................................18
§3. δL EC ..................................................20
§4. H and B ................................................22
§5. δH and C ..............................................23
§6. H vs. δH and B vs. C ..................................26
§7. ∫Σ H= -NP+ (1/2)λJ ..................................28
§8. Covariant Differentials ................................30
Chapter 4. Application in the Linearized theory of gravity ..34
§1. Introduction ...........................................34
§2. Basic quantities in weak- field limit ..................34
§3. Orders of magnitude ....................................40
§4. Quasilocal Quantities in Weak Fields ...................41
Chapter 5. Evaluation of the COM moment .....................44
§1. First- order expansion of quantities; Connections ......44
i. Metrics ...............................................44
ii. Metric Densities ......................................45
iii. △η, etc. ............................................46
iv. Connections ...........................................46
v. Expansion of N and DN .................................48
§2. Various B forms ........................................48
i. The Komar- type expressions ...........................49
ii. The Freud- type expressions ...........................50
§3. Evaluation of the conserved quantities .................51
i. P0 ....................................................52
ii. Pj’s and Jjk’s ........................................58
iii. J0j’s: the COM moments ................................58
Chapter 6. Conclusion and Discussion ........................65
References ..................................................68


[ADM] R.Arnowitt, S.Deser and C.W.Misner, Phys. Rev. 122 (1961), 997 [BO] R.Beig and N.O’Murchadha, Ann. Phys. 174 (1987) 463-98 [BY] J.D.Brown and J.W.York, Jr., Phys. Rev. D 47 (1993) 1407-19 [CNC99] C.C.Chang, J.M.Nester and C.M.Chen, Phys. Rev. Lett. 83 (1999) 1897-901 [CNC00] C.C.Chang, J.M.Nester and C.M.Chen, Gravitation and Astrophysics, (World Scientific, 2000) pp163-173 [Che] C.M.Chen, Quasilocal quantities for gravity theories (MSc thesis, 1994, NCU, unpublished) [Cha] C.C.Chang, The localization of gravitational energy — pseudotensors and quasilocal expressions (MSc thesis, 1998, NCU, unpublished) [CN99] C.M.Chen and J.M.Nester, Class.Quantum Grav. 16 (1999) 1279 [CN00] C.M.Chen and J.M.Nester, Gravitation & Cosmology 6 (2000) 257 [Dou] N.A.Doughty, Lagrangian interaction (Singapore, Addison-Wesley, 1990) [Fr] P.Freud, Ann. Math. 40 (1938) 417 [Ha] K.Hayashi and T.Shirafuji, Prog. Phys. 64 (1980), 866, 883, 1435, & 2222 [He76] F.W.Hehl, P.von der Heyde, G.D.Kerlik and J.M.Nester, Rev. Mod. Phys. 48 (1976) 393 [He95] F.W.Hehl, J.D.McCrea, E.W.Mielke and Y.Ne’eman, Phys. Rep. 258 (1995) 1 [KBL] J.Katz, J.Bicak and D. Lynden-Bell, Phys. Rev. D 55 (1997) 5957 [Ko] A.Komar, Phys. Rev. 113 (1959) 934 [Mo] C.MØller, Ann. Phys. (N.Y.) 12 (1961), 118 [MTW] C.W.Misner, K.Thorne, and J.A.Wheeler, Gravitation (San Francisco, Freeman, 1973) [Vu] K.H.Vu, Quasilocal energy- momentum and energy momentum for Teleparallel gravity (MSc thesis, 2000, NCU, unpublished)

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