Introducing Einstein's Relativity

Description

This textbook provides students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject

• Breaks down a complicated subject into simple logical steps for bite-sized, accessible learning
• Supports visual-based learning and contains over 250 diagrams
• Text is reinforced by exercises that give the reader confidence and develop understanding

New to this edition

• Extended the chapter on the structure of the field equations These go into more detail about the passage from the geometrical formulation of Einstein's equations to a description in terms of evolution equations. This is needed in attacking outstanding theoretical problems such as `cosmic censorship' as well as constructing stable numerical relativity codes to simulate events such as colliding black holes.
• Considerable extended the chapter on gravitational waves to include a description of both the sources and detection of gravitational waves. We now have about the structure of the universe. For example, we now know considerably more about gravitational waves from the direct measurements by the LIGO gravitational wave observatories of radiation from colliding black holes, as well as the indirect measurements of gravitational radiation coming from the orbits of binary pulsars.
• New chapter on modern cosmology. We also have much more accurate information about the expansion of the universe and the cosmic microwave background. These developments have resulted in a new chapter describing the modern approach to cosmology in which one uses experimental evidence to determine the cosmological parameters of our universe
• New chapter on the 3+1 and 2+2 formalisms

About the Author(s)

Ray d'Inverno, Emeritus Professor, University of Southampton, and James Vickers, Emeritus Professor, University of Southampton

Professor 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.

Table of Contents

1:The Organisation of the Book
A: Special Relativity
2:The k-Calculus
3:The Key Attributes of Special Relativity
4:The Elements of Relativistic Mechanics
B: The Formalism of Tensors
5:Tensor Algebra
6:Tensor Calculus
7:Integration, Variation, and Symmetry
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 sSlution
16:Classical Experimental Tests of General Relativity
D: Black Holes
17:Non-Rotating Black Holes
18:Maximal Extension and Conformal Compactification
19:Charged Black Holes
20:Rotating Black Holes
E: Gravitational Waves
21:Linearized Gravitational Waves and their Detection
22:Exact Gravitational Waves
23:Radiation from an Isolated Source
F: Cosmology
24:Relativistic Cosmology
25:The Classical Cosmological Models
26:Modern Cosmology
Answers to Exercises
Selected Bibliography
Index