臺灣博碩士論文加值系統

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

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