The Geometry of Spacetime       James J. Callahan

img1.gif

  1. Relativity before 1905
  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

 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

Relativity : the general theory

  1. Essential tensor formulae for Riemannian Spacetime
  2. The world-functio
  3. Chronometry in Riemannian Spacetime
  4. The material continuum
  5. Some properties of Einstein fields
  6. Integral conservation laws  and equations of motion
  7. Fields with spherical symmetry
  8. Some special universes
  9. Gravitational waves
  10. Electromagnetism
  11. Geometrical Optics