Texts and Readings in Physical Sciences

This introductory textbook on the general theory of relativity presents a solid foundation for those who want to learn about relativity. The subject is presented in a physically intuitive, but mathematically rigorous style. The topic of relativity is covered in a broad and deep manner. Besides, the aim is that after reading the book a student should not feel discouraged when he opens advanced texts on general relativity for further reading.






The book consists of three parts:

• An introduction to the general theory of relativity.
• Geometrical mathematical background material.
• Topics that include the action principle, weak gravitational fields and gravitational waves, Schwarzschild and Kerr solution, and the Friedman equation in cosmology.

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 graduates and graduates, but also for established researchers wishing to be educated about the field.
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. Additional Topics in Geometry

III. Gravitation:
11. The Einstein Equation
12. General Features of Spacetime
13. Weak Gravitational Fields
14. Schwarzschild and Kerr Solutions
15. Cosmology
16. Special Topics