Relativity. Special, General and Cosmological
This book covers many important topics from special relativity, general relativity and cosmology. The language of tensor fields is introduced early on and used systematically, and the necessary knowledge is recalled in a short and clearly written summary. The reader will find here a clear and understandable explanation of the physical principles behind the theory of relativity and its use in cosmology. Each chapter of the book ends with exercises, around 300 in total, which form an important part of the book. The special relativity part starts with the Lorentz group, relativistic kinematics and optics. Four-vectors are used to describe relativistic particle mechanics, and the Maxwell equations are formulated in terms of Minkowski tensor fields. After introducing basic ideas of general relativity and formulating the Einstein equations in terms of (pseudo)-Riemannian geometry, the author discusses properties of the Schwarzschild space, black holes, plane waves, (anti-)de Sitter spaces, and linearised gravity. The book ends with three chapters on cosmology, including many properties of Friedman-Robertson-Walker universes.
This book is a pleasure to read. It will be an excellent source, allowing the reader to build a proper intuition and to understand the basic facts of the theory. The level of mathematical knowledge required is very modest, so it should be useful for students at graduate level, both physicists and mathematicians.