Introduction to General Relativity

Abstract

General Relativity, Einstein's theory of gravity, has had an interesting journey in terms of its role in modern physics since its birth almost a century ago. At first, it was considered highly mathematical, abstract, and not essential for understanding the physics of the Universe. In the words of Jim Lovell in Apollo 13: `We just put Sir Isaac Newton in the driver's seat', if Newtonian gravity could send men to the moon, did we really need Einstein? This status was reflected in the paucity of good textbooks. When this reviewer began to teach herself relativity over 30 years ago, the task was rather daunting!Roughly 25 years ago the situation began to change. In part, progress in understanding and applying string theory increasingly required a really good grounding in gravity, indeed half of string theorists these days seem to be relativists in disguise! Yet it is not only in formal theoretical physics that gravity has become more central: developments in observational cosmology also need a good grounding of Einstein gravity to completely understand and extract the physics of both the early and the late Universe. Finally, as we move to an era of gravitational-wave astronomy, the role of General Relativity (GR) as a practical experimental tool has emerged. As a result, we now have many textbooks on GR to choose from, and any new textbook must be judged in this context.Ryder's book follows a path familiar to many British students of GR, it starts by building up a picture of space-time and arguing that to include gravitational effects, we must have a concept of curved space-time. He then reviews the necessary tensor calculus, deriving the Einstein field equations from the Newtonian limit. He then turns to the consequences of Einstein gravity for our solar system, before looking more generally at black holes, gravitational radiation and cosmology. As such, the book has a clear and logical structure, although physics students might well find it abstract at times. The book is not overly mathematical however, in fact, I felt it introduced only that mathematics necessary for the physics, and the discussion was only as formal and rigorous as needed.The real strength of the book however, and what I most enjoyed while reading it, was the way Ryder had patently taken time to dig into and discuss the little issues of relativity, and to patiently make them explicit to the reader. When is a space flat for example? We know what it means, but if presented with a metric, can we tell? By walking the reader through examples of different coordinates for flat space, Ryder gives an indispensible tutorial on how we look at, and calculate with, different coordinate systems. For a student meeting relativity for the first time this type of clear and explicit worked example should be extremely valuable.The book includes many diagrams, which complement the text and enhance the clarity of the explanations. Exercises are included at the end of chapters, as well as worked examples and useful insights throughout the text.Overall, I would recommend this book to any new student of GR. It is clear, insightful, and interesting to read. The book is best suited to students with a strong, but not overpowering, mathematical background. Pure mathematicians may be irritated by the economies made in the mathematics, and physicists may be frustrated at the level of mathematics, but if you need to use GR and want to learn it at a level where you can become expert at it, then this book should answer your needs.