General Relativity, Astrophysics, and Cosmology

I. The General Theory of Relativity.- 1. Introduction.- 2. Tensor Calculus and Riemannian Geometry.- 3. Einstein’s Field Equations.- 4. The Schwarzschild Metric and Crucial Tests.- 5. Electromagnetism in General Relativity.- 6. Axially Symmetric Fields.- 7. The Kerr Metric or the Rotating Black Hole.- 8. The Energy—Momentum Pseudotensor of the Gravitational Field and Loss of Energy by Gravitational Radiation.- 9. Analysis of the Observational Data of the Hulse—Taylor Pulsar. Confirmation of the Einstein Quadrupole Radiation Formula.- II. Relativistic Astrophysics.- 10. White Dwarf Stars.- 11. Stellar Evolution, Supernovae, and Compact Objects.- 12. Pulsars.- 13. Spherically Symmetric Star Models.- 14. Black Holes.- 15. Accretion onto Compact Objects.- III. Cosmology.- 16. The Standard Cosmological Model.- 17. The Singularity Problem.- 18. Thermal History of the Universe—Cosmological Nucleosynthesis.- 19. Structure Formation in the Universe.- 20. Grand Unified Theory and Spontaneous Symmetry Breaking.- 21. The Inflationary Scenario.- 22. Concluding Remarks.- Appendix. Differential Forms.- A.1. Introductory Ideas and Definitions.- A.2. Connection 1-Forms and Ricci Rotation Coefficients.- A.3. Cartan’s Equations of Structure.- A.4. Bianchi Identities and Symmetry Properties of the Riemann—Christoffel Tensor.- A.5. An Example of the Calculation of the Riemann—Christoffel Tensor.- References.