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This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.

Einstein's General Theory of Relativity: With Modern Applications in Cosmology

I. Introduction: Newtonian Physics and Special Relativity- 1. Relativity Principals and Gravitation 2. The Special Theory of Relativity II. The Mathematics of the General Theory of Relativity- 3. Vectors, Tensors, and Forms 4. Basis Vector Fields and Metric Tensor 5. Non-inertial Reference Frames 6. Differentiation, Connections and Integration 7. Curvature II. Einstein's Field Equations- 8. Einstein's Field Equations 9. The Linear Field Approximation 10. The Schwarzschild Solution and Black Holes IV. Cosmology- 11. Homogeneous and Isotropic Universe Models 12. Universe Models with Vacuum Energy 13. An Anisotropic Universe V. Advanced Topics- 14. Covariant decomposition, Singularities, and Canonical Cosmology 15. Homogeneous Spaces 16. Israel's Formalism: The metric junction method 17. Brane-worlds 18. Kaluza-Klein Theory VI. Appendices- A. Constrants of Nature B. Penrose diagrams C. Anti-de Sitter spacetime D. Suggested further reading