General theory of relativity: a mathematical approach

Includes bibliographical references and index.

The general theory of relativity, Einstein's theory of gravitation, has been included as a compulsory subject in undergraduate and graduate courses in Physics and Applied Mathematics all over the world. However, the physics-first approach that is taken by many textbooks is not universally used, as the approach often depends on the instructors' or students' background. Conceived from the lecture notes made by the author over a teaching career spanning 18 years, this book introduces the general theory of relativity for advanced students with a strong mathematical background. The proposed book takes a 'math-first approach' for which the mathematical formalism comes first and is then applied to physics. It presents a concise yet comprehensive and structured understanding of general theory of relativity. The book discusses the mathematical foundation of general theory of relativity and focuses heavily on topics such as tensor calculus, geodesics, Einstein field equations, linearized gravity, Lie derivatives and their applications, causal structure of space-time, rotating black holes and a basic knowledge of cosmology and astrophysics. All of this is explained through a large number of worked examples and exercises.