Introducing Einstein’s Relativity

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

Table of 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

About the Authors

Ray d’Inverno, Emeritus Professor, University of Southampton,James Vickers, Emeritus Professor, University of Southampton

Ray d’Inverno is Emeritus Professor in General Relativity at the University of Southhampton. A pioneer in the use of computer algebra in general relativity, Professor d’Inverno developed the early system LAM (Lisp Algebraic Manipulator), which was a precursor to Sheep, the system most used to date in the study of exact solutions and their invariant classification. He also developed the 2+2 formalism for analysing the initial value problem in general relativity. The formalism has also been used to provide a possible route towards a canonical quantization programme for the theory. In addition, he worked in numerical relativity (solving Einstein’s equations numerically on a computer) and with others set up the CCM (Cauchy-Characteristic Matching) approach, which is still used in this increasingly important field.

James Vickers is an Emeritus Professor of Mathematics at the University of Southampton and has published extensively on general relativity. His early research was on the structure of weak singularities in relativity and more recently he has given proofs of both the Penrose and Hawking singularity theorems for low-regularity spacetimes. These show that the singularities predicted by these theorems must be accompanied by unbounded curvature. He has also worked on the asymptotic structure of space-time and used spinors to prove the positivity of the Bondi mass.