An Introduction to General Relativity (Paperback)

Preface; 1. Introduction; 2. Vectors and tensors in flat three-space; 3. Aspects of special relativistic geometry; 4. Tensor analysis on manifolds; 5. Covariant differentiation; 6. Properties of the Riemann tensor; 7. Riemannian geometry; 8. The Lie derivative; 9. Geodesics; 10. Geodesic deviation; 11. Differential forms; 12. The transition from Newtonian theory; 13. Einstein's field equations; 14. The slow motion approximation; 15. The Schwarzschild solution; 16. Gravitational red-shift and time dilation; 17. The geodesic equation for the Schwarzschild solution; 18. Classical tests; 19. The extended Schwarzschild solution; 20. Black holes and gravitational collapse; 21. Interior solutions; 22. The Kerr solution; 23. Homogeneous and isotropic three-spaces; 24. Cosmology: kinematics; 25. Cosmology: dynamics; 25. Anisotropic cosmologies; Index.