Introducing Einstein's Relativity: A Deeper Understanding

Description

There is little doubt that Einstein's theory of relativity captures the imagination. Not only has it radically altered the way we view the universe, but the theory also has a considerable number of surprises in store. This is especially so in the three main topics of current interest that this book reaches, namely: black holes, gravitational waves, and cosmology. The main aim of this textbook is to provide students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject. Indeed, the book follows Einstein in that it introduces the theory very much from a physical point of view. After introducing the special theory of relativity, the basic field equations of gravitation are derived and discussed carefully as a prelude to first solving them in simple cases and then exploring the three main areas of application. This new edition contains a substantial extension content that considers new and updated developments in the field. Topics include coverage of the advancement of observational cosmology, the detection of gravitational waves from colliding black holes and neutron stars, and advancements in modern cosmology. Einstein's theory of relativity is undoubtedly one of the greatest achievements of the human mind. Yet, in this book, the author makes it possible for students with a wide range of abilities to deal confidently with the subject. Based on both authors' experience teaching the subject this is achieved by breaking down the main arguments into a series of simple logical steps. Full details are provided in the text and the numerous exercises while additional insight is provided through the numerous diagrams. As a result this book makes an excellent course for any reader coming to the subject for the first time while providing a thorough understanding for any student wanting to go on to study the subject in depth. Dedications Foreword • Roger Penrose Contents 1 The organization of the book Part A: Special Relativity 2 The k-calculus 3 The key attributes of special relativity 4 The elements of relativistic mechanics Part B: The Formalism of Tensors 5 Tensor algebra 6 Tensor calculus 7 Integration, variation, and symmetry Part C: General Relativity 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 Part D: Black Holes 17 Non-rotating black holes 18 Maximal extension and conformal compactification 19 Charged black holes 20 Rotating black holes Part E: Gravitational Waves 21 Linearized gravitational waves and their detection 22 Exact gravitational waves 23 Radiation from an isolated source Part F: Cosmology 24 Relativistic cosmology 25 The classical cosmological models 26 Modern cosmology Answers to exercises Selected bibliography Index