4. Contravariant
and Covariant Vector Fields ................................................24
5. Tensor
Fields....................................................................................................35
6. Riemannian
Manifolds...................................................................................40
7. Locally
Minkowskian Manifolds: An Introduction to
Relativity.............50
8. Covariant
Differentiation...............................................................................61
9. Geodesics and
Local Inertial
Frames.............................................................69
10. The Riemann
Curvature
Tensor..................................................................82
11. A Little More
Relativity: Comoving Frames and Proper Time ...............94
12. The Stress
Tensor and the Relativistic Stress-Energy
Tensor................100
13. Two Basic
Premises of General
Relativity................................................109
14. The Einstein
Field Equations and Derivation of Newton's Law...........114
15. The
Schwarzschild Metric and Event Horizons ......................................124
16. White Dwarfs,
Neutron Stars and Black Holes, by Gregory C. Levine131
References and
Further Reading................................................................138