本論文的主要工作是介紹廣義相對論及黑洞。第壹章中我們介紹狹義及廣義相對論發展過程的歷史背景，以此了解到當時的物理遇到了何種問題而需要相對論。第貳章是介紹廣義相對論的兩條基本假設，並由此兩條基本假設開始，發展出廣義相對論的理論。第參章所介紹的是廣義相對論的實驗驗證，以這些實驗證明了廣義相對論的成功。廣義相對論中，黑洞是我們得到的一個重要結果，它為廣義相對論預言存在的一種天體，具有相當特殊的性質。因此接下來我們介紹兩個類型的黑洞，第肆章介紹的是史瓦西黑洞，第伍章介紹的是克爾黑洞。最後一章為總結第貳章到第伍章所介紹的廣義相對論及黑洞。並相信將來可以有著更加完善的理論以描述自然界。

The main purpose of this thesis is to introduce the theory of  general relativity and the black hole. In the first chapter, the history of the development of the theory of special and general relativity is introduced, to understand the problems that people encountered and to explain the reasons why the theory of general relativity was needed. Then, in the second chapter, we show how to derive general relativity from two fundamental postulates that are the core of this theory. The decisive experiments which support the theory are presented in the third chapter. The black hole, which motivates this research,is an astronomical object which is an important result predicted by general relativity with some strange properties. Hence, two important kinds of the black holes, Schwarzschild and Kerr black hole, are introduced in the fourth and fifth chapter respectively. The last chapter is the conclusion for 
this thesis. It is believed that in the future a better theory will be established to describe the nature.

第壹章 簡介................................................1
 第貳章 廣義相對論的介紹...................................3
  2-1 廣義相對論的基本假設.................................3
  2-2 張量代數.............................................5
  2-3 度規張量.............................................8
  2-4 彎曲空間的座標轉換...................................9
  2-5 平移................................................10
  2-6 協變微分............................................11
  2-7 短程線..............................................15
  2-8 曲率張量............................................17
  2-9 愛因斯坦場方程式....................................19
第參章  廣義相對論的驗證..................................23
  3-1 史瓦西解............................................23
  3-2 引力紅移............................................27
  3-3 水星近日點的進動....................................29
  3-4 引力場下光線的偏折..................................33
  3-5 雷達回波延遲........................................36
第肆章  黑洞..............................................39
  4-1 簡介................................................39
  4-2 史瓦西黑洞..........................................40
  4-3 Eddington-Finkelstein座標...........................43
  4-4 粒子落入黑洞........................................46
第伍章  克爾黑洞..........................................49
  5-1 零標架..............................................49
  5-2 克爾解..............................................52
  5-3 轉動的黑洞..........................................56
第陸章  結論..............................................63
參考資料..................................................65

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