廣義相對論

廣義相對論中的數學   丘成桐

The Geometry of Spacetime       James J. Callahan

img1.gif 

  1. Relativity before 1905      [Galilean tranformation]
  2. Special Relativity---Kinematics(運動學)
  3. Special Relativity---Kinetics(動力學)
  4. Arbitrary Frames
  5. Surfaces and Curvature
  6. Intrinsic Geometry
  7. General Relativity
  8. Consequences

習作  勘誤   Errata for the Solutions   [ResearchGate]

General Relativity for Mathematicians      Rainer K. Sachs   H.Wu(伍鴻熙)

    img1.gifimg2.gif                                                  [廣義相對論]

 0. Preliminaries

  1. Spacetimes
  2. Observes
  3. Electromagnetism and Matter
  4. The Einstein field equation
  5. Photons
  6. Cosmology
  7. Further applications
  8. Optional exercises : relativity
  9. Optional exercises : Newtonian analogues

Relativity :(1) the special theory   (2) the general theory      J.L.Synge

img1.gifJohn L. Synge 1897-1995

 愛爾蘭(Irish)數學家與物理學家  Synge's theorem 1936年 : M is a closed Riemannian manifold with positive sectional curvature

If M is even-dimensional and orientable , then M is simply connected.

If M is odd-dimensional ,the it is orientable.

 Relativity : the special theory

  1. The Space-time continuum and the separation between events
  2. Introduction to the special theory
  3. Space-time diagrams
  4. The Lorentz transformation
  5. Applications of the Lorentz transfirmation
  6. Mechanics of a particle and collision problems
  7. Mechanics of a discrete system
  8. Mechanics of a continuum
  9. The electromagnetic field in vacuo
  10. Fields and Charges
  11. Appendix