廣義相對論的準局域量的小球極限; Quasilocal Conserved Quantities For General Relativity In Small Regions

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题名:	廣義相對論的準局域量的小球極限;Quasilocal Conserved Quantities For General Relativity In Small Regions
作者:	孫綱;Gang Sun
贡献者:	物理研究所
关键词:	小球極限;準局域;small region limit;quasilocal
日期:	2005-06-21
上传时间:	2009-09-22 10:55:46 (UTC+8)
出版者:	國立中央大學圖書館
摘要:	引力能量是個長期被關注的問題。到目前為止，有幾種方法可以處理這個問題，但最好的辦法是使用準局域的概念。中央大學幾何物理學研究團隊已經發展出他們的準局域的理論－協變哈彌爾頓架構，並且在類光和類空無窮遠獲得好的計算結果。不過，實際上目前在大尺度的真空中極限僅僅是檢驗了弱場線性引力的準局域表達。除了無窮遠的情況，還存在另一類的極端情形－小區域的極限。真空的小球極限是對準局域的理論的重要測試，這種測試是檢驗引力場第一階的非線性部分。這篇論文的目的是去測試協變哈彌爾頓架構在小範圍的極限。在第一章裡，我們將介紹準局域的基本概念和相關的應用；在第二章，我們將告訴讀者什麼是協變哈彌爾頓架構並且推導它；在第三章，我們將介紹能量、動量、角動量和質心矩的一般性概念並展示物理量和守恆間的關係；在之後的章節，用準局域的方法計算小球極限的量值過程將會詳細地被說明，此處，我們不但考慮了真空，也給出了含有物質場的情況；最後一章裡，我們會討論計算結果所隱含的意義，而這些結果告訴我們對四種協變哈彌爾頓的表示式僅有一種給出了正能量。 Gravitational energy has been a concern for a long time. There are several ways to deal with the problem, but the best way is the quasilocal approach. The NCU group has been developing their quasilocal approach – the covariant Hamiltonian formalism, and has obtained good results for spatial and null infinity. In addition to these infinite cases; there is another limit case – the small region limit. The small region vacuum limit provides an important test of the quasilocal expression. Whereas the large scale asymptotic limit tests only the weak field linearized part of the expression, the small scale vacuum limit probes the next order non-linear part. In this thesis the purpose is to test the covariant Hamiltonian formalism in the small region limit. In the first chapter, we will introduce the basic ideas of the quasilocal method and some related ideas. In chapter two, we will show the readers what the covariant Hamiltonian formulism is and how to derive it. In the chapter three, we will introduce some general concepts about energy-momentum, angular momentum and center-of-mass moment, and the relation between these physical quantities and conservation. In the next chapter, the detailed procedure on how to get quasilocal values in the small region limit, including the vacuum case and matter case, using covariant Hamiltonian formulism will follow. In the final chapter, we will discuss the meaning of our results and conclude that only one of the four covariant Hamiltonian expressions gives positive energy in the first non-linear order. Finally we will comment some deficiencies.
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