1. How the theory of relativity came into being (a brief historical sketch) Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries 3. Tensors, tensor densities 4. Covariant derivatives 5. Parallel transport and geodesic lines 6. Curvature of a manifold: flat manifolds 7. Riemannian geometry 8. Symmetries of Rieman spaces, invariance of tensors 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs 10. The spatially homogeneous Bianchi-type spacetimes 11. The Petrov classification by the spinor method Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory 14. Spherically symmetric gravitational field of isolated objects 15. Relativistic hydrodynamics and thermodynamics 16. Relativistic cosmology I: general geometry 17. Relativistic cosmology II: the Robertson-Walker geometry 18. Relativistic cosmology III: the Lemaître-Tolman geometry 19. Relativistic cosmology IV: generalisations of L-T and related geometries 20. The Kerr solution 21. Subjects omitted in this book References.
1. How the theory of relativity came into being (a brief historical sketch) Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries 3. Tensors, tensor densities 4. Covariant derivatives 5. Parallel transport and geodesic lines 6. Curvature of a manifold: flat manifolds 7. Riemannian geometry 8. Symmetries of Rieman spaces, invariance of tensors 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs 10. The spatially homogeneous Bianchi-type spacetimes 11. The Petrov classification by the spinor method Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory 14. Spherically symmetric gravitational field of isolated objects 15. Relativistic hydrodynamics and thermodynamics 16. Relativistic cosmology I: general geometry 17. Relativistic cosmology II: the Robertson-Walker geometry 18. Relativistic cosmology III: the Lemaître-Tolman geometry 19. Relativistic cosmology IV: generalisations of L-T and related geometries 20. The Kerr solution 21. Subjects omitted in this book References.
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