廣義相對論 [An Introduction to Riemannian Geomery] Leonor Godinho . Jose Natario


6.1 Galileo Spacetime

6.2 Special Relativity

6.3 The Cartan Connection

6.4 General Relativity

6.5 The Schwarzschild Solution

6.6 Cosmology

6.7 Causality

6.8 Hawking Singularity Theorem

6.9 Penrose Singularity Theorem

  1. The Geometry of Spacetime      James J.Callahan
  2. General Relativity for Mathematicans      Rainer K.Sachs   Hung-Hsi Wu(伍鴻熙)
  3. General Relativity :An Introduction for Physicists      Michael.P.Hobson  Geoerge.P.Efstathiou  Anthony.N.Lasenby
  4. Lecture Notes on General Relativity        Matthias Blau
  5. Unsolved Problems      Florentin Smarandache   Fu Yuhua  Zhao Feng-Juan

[何謂廣義相對論] (原文) [Problems of gravity]

廣義相對論中的純量曲率      正質量定理      廣義相對論中的量子效應

 張海潮先生

  1. 水星近日點進動(precession of perihelion)
  2. 光經過太陽的偏折角度
  3. 紅位移(redshift)
  4. 狹義相對論

丘成桐先生

  1. 時空幾何與廣義相對論中的質量
  2. 廣義相對論中數學]    [Calabi conjecture]

重力場方程

Hermann Weyl 引入規範場論(gauge theory)

廣義相對論中的質量 孤立物理系統的質量是否為正,是廣義相對論的一個重要問題。
如果質量不恆為正,系統會變得不穩定,而廣義相對論的正確性也變得難以確保。

重力輻射      事件視界望遠鏡 EHT(event horizon telescope)


Black Holes :

  Non-rotating J=0 Rotating
uncharged (Q=0) Schwarzschild Kerr
chargedd Reissner-Nordstrom Kerr-Newman
  1. Rotating Black Holes The Geometry of Kerr Spacetime      Anusar Farooqui
  2. Kerr Black Holes(1963)     Chris Reynolds
  3. The kerr Spacetime : A brief introduction      Matt Visser [arXiv]
  4. The geometry of Kerr Black Hole                  Barrett O'Niell

Killing vector field的metric是Isometry(等距同構)   Kerr metric

ergosphere(動圈)

 

Wormhole :

Morris-Thorne wormhole      geodesics of MT-wormhole     geodesics of BH with charge

Dark matter :