Spacetime, Geometry and Gravitation

Contents: I. Spacetime: 1. Introduction. 2. What is Curvature? 3. General relativity basics. 4. Spherically symmetric gravitational field. II. Geometry: 5. Vectors and Tensors. 6. Inner Product. 7. Elementary Differential Geometry. 8. Connection and Curvature. 9. Riemannian geometry. 10. Some More Geometry. III. Gravitation: 11. The Einstein Equation. 12. General features of spacetime. 13. Weak Gravitational fields. 14. Schwarzschild and Kerr solutions. 15. Cosmology."This textbook introduces a student to the physical as well as the mathematical foundations of general relativity.

This textbook introduces a student to the physical as well as the mathematical foundations of general relativity.

Following an introduction to the general theory of relativity, the required geometrical and mathematical background is presented in detail. The third part of the book includes a range of topics such as the action principle, weak fields, gravitational waves, the Schwarzschild and Kerr solutions, the Friedman equation, the Gauss-Codacci equations and the Raychaudhuri equation. Following an introduction to the general theory of relativity, the required geometrical and mathematical background is presented in detail. The third part of the book includes a range of topics such as the action principle, weak fields, gravitational waves, the Schwarzschild and Kerr solutions, the Friedman equation, the Gauss-Codacci equations and the Raychaudhuri equation.
A special feature of the book is the inclusion of many exercises (provided with solutions) so as to help the student acquire a better understanding of the material. A student who has followed the book should be able to study other advanced texts and papers in the area of general relativity without extra preparation.

The book is suitable for advanced undergraduate and graduate students. Established researchers will find the presentation of many topics novel, and thus the text can also serve as a reference book."