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The theory of relativity stands out as one of the greatest achievements in science. The special theory , which did not include gravity, was put forward by Einstein in 1905 to explain many troubling facts that had arisen in the study of electricity and magnetism. In particular, his postulate that the speed of light in vacuum is the same constant seen by all observers forced scientists to throw away many closely held commonsense assumptions, such as the absolute nature of the passage of time. In short, the theory of relativity challenges our notions of what reality is, and this is one of the reasons why the theory is so interesting. Einstein published the general theory of relativity, which is a theory about gravity, about a decade later. This theory is far more mathematically daunting, and perhaps this is why it took Einstein so long to come up with it. This theory is more fundamental than the special theory of relativity; it is a theory of space and time itself, and it not only describes, it explains gravity. Gravity is the distortion of the structure of spacetime as caused by the presence of matter and energy, while the paths followed by matter and energy (think of bending of passing light rays by the sun) in spacetime are governed by the structure of spacetime. This great feedback loop is described by Einstein s eld equations. This is a book about general relativity. There is no getting around the fact that general relativity is mathematically challenging, so we cannot hope to learn the theory without mastering the mathematics. Our hope with this book is to demystify that mathematics so that relativity is easier to learn and more accessible to a wider audience than ever before. In this book we will not skip any of the math that relativity requires, but we will present it in what we hope to be a clear fashion and illustrate how to use it with many explicitly solved examples. Our goal is to make relativity more accessible to everyone. Therefore we hope that engineers, chemists, and mathematicians or anyone who has had basic mathematical training at the college level will nd this book useful. And
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Copyright 2006 by The McGraw-Hill Companies, Inc. Click here for terms of use.
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of course the book is aimed at physicists and astronomers who want to learn the theory. The truth is that relativity looks much harder than it is. There is a lot to learn, but once you get comfortable with the new math and new notation, you will actually nd it a bit easier than many other technical areas you have studied in the past. This book is meant to be a self-study guide or a supplement, and not a fullblown textbook. As a result we may not cover every detail and will not provide lengthly derivations or detailed physical explanations. Those can be found in any number of ne textbooks on the market. Our focus here is also in demystifying the mathematical framework of relativity, and so we will not include lengthly descriptions of physical arguments. At the end of the book we provide a listing of references used in the development of this manuscript, and you can select books from that list to nd the details we are leaving out. In much of the material, we take the approach in this book of stating theorems and results, and then applying them in solved problems. Similar problems in the end-of chapter quiz help you try things out yourself. So if you are taking a relativity course, you might want to use this book to help you gain better understanding of your main textbook, or help you to see how to accomplish certain tasks. If you are interested in self-study, this book will help you get started in your own mastery of the subject and make it easier for you to read more advanced books. While this book is taking a lighter approach than the textbooks in the eld, we are not going to cut corners on using advanced mathematics. The bottom line is you are going to need some mathematical background to nd this book useful. Calculus is a must, studies of differential equations, vector analysis and linear algebra are helpful. A background in basic physics is also helpful. Relativity can be done in different ways using a coordinate-based approach or differential forms and Cartan s equations. We much prefer the latter approach and will use it extensively. Again, it looks intimidating at rst because there are lots of Greek characters and fancy symbols, and it is a new way of doing things. When doing calculations it does require a bit of attention to detail. But after a bit of practice, you will nd that its not really so hard. So we hope that readers will invest the effort necessary to master this nice mathematical way of solving physics problems.
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