INTRODUCING EINSTEIN'S RELATIVITY: a deeper understanding

The aim of this book is to provide the reader with a sound mathematical introduction to Einstein's theory of relativity, both special relativity and general relativity, as well as an understanding of the physical insights needed to explore the subject and the principles that guided Einstein in his search for the general theory of relativity. A feature of the book is that it has the numerous illustrative diagrams and exercises (of varying degrees of difficulty) which help the reader develop insight and confidence in using the mathematics. The book starts out by introducing special relativity and then the mathematics required for the rest of the book is carefully introduced. The principles underlying general relativity are introduced and it is shown how these lead to the basic field equations. These are then discussed and solved in some simple but physically important situations. The final three sections deal with the major applications of the theory and cover the topics of black holes, gravitational waves, and cosmology. These sections further develop the theory but also relate the theoretical predictions to current observations. These include the recent observation of gravitational waves by LIGO, evidence for supermassive black holes at the centre of most galaxies and the detailed observations of the cosmic microwave background that provide the evidence for modern cosmology.

1 The organization of the book -- 2 The k-calculus -- 3 The key attributes of special relativity -- 4 The elements of relativistic mechanics -- 5 Tensor algebra -- 6 Tensor calculus -- 7 Integration, variation, and symmetry -- 8 Special relativity revisited -- 9 The principles of general relativity -- 10 The field equations of general relativity -- 11 General relativity from a variational principle -- 12 The energy-momentum tensor -- 13 The structure of the field equations -- 14 The 3+1 and 2+2 formalisms -- 15 The Schwarzschild solution -- 16 Classical experimental tests of general relativity -- 17 Non-rotating black holes -- 18 Maximal extension and conformal compactification -- 19 Charged black holes -- 20 Rotating black holes -- 21 Linearized gravitational waves and their detection -- 22 Exact gravitational waves -- 23 Radiation from an isolated source -- 24 Relativistic cosmology -- 25 The classical cosmological models -- 26 Modern cosmology