21 of 21 people found the following review helpful:
5.0 out of 5 stars
All the Math You Need for GR, April 28, 2007
This review is from: Tensors, Relativity, and Cosmology (Hardcover)
This book, alone, was what got me through my General Relativity course. The text we were using didn't include much math, and the professor didn't want to discuss the mathematical aspects of what we were doing. So I came upon this book armed with a vague physical understanding, but mathematically clueless. Fortunately, this book seems to have been written for precisely such a situation!
In a remarkably clear and concise manner, this book manages to:
- introduce the notations that are commonly used
- demonstrate how a physical system can be represented using the new formalisms
- outline the common mathematical operations that can be performed under this formalism
- describe how these operations are different from similar operations that the reader is already familar with
- show how these mathematical operations are physically relevant to a particular system
The other mathematical texts on this topic all seem to start off slowly with several chapters full of things that, as a physicist, I don't particularly want to know about. This book, by contrast, simply skips right to the parts that are relevant to relativistic calculations, and as a result the reader need not waste time trying to understand mathematical concepts that will not be useful to him.
In short, it's absolutely perfect if you need help with the mathematical aspects of relativity. Its physical explanations are brief, however, so if it's the physical concepts themselves that are troubling you, it might be better to start with a more descriptive book.
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6 of 7 people found the following review helpful:
5.0 out of 5 stars
One of the best, January 4, 2011
This review is from: Tensors, Relativity, and Cosmology (Hardcover)
This book starts out with a walk through the gymnastics of manipulating tensor indices's. Tensors can have any number of indices's attached to them. Learning to work with these indices's comes up many times for example in QFT(Quantum Field Theory). It is really basic, but until you see it done a number of time(as in this book) it can be quite confusing. This book teaches you to do this, and does a very good job. This includes the famous Einstein summation convention.
The book also covers co-variant derivatives, which are really important for taking derivatives in curvilinear coordinate since the unit or basis vectors change. Again the book does an excellent job of explaining this. This leads to the next subject of Christoffel Symbols, which come up when taking a co-variant derivative. The book explains these in terms easy to understand.
The book then goes into differential geometry. This is where the book really shines. This section is really a critical part, since you will need the ideas learned here to derive Einstein Field Equations. There is just the right amount of theory here so you can understand what is going on under the hood, but not too so much that you lose all prospective of what is going on.
Then this book covers special relativity. The book really shines here since the approach is a mature one, not watering down the math, but not over doing it either. The book has now taught you about Tensor Analysis, so the author can use it to cover special relativity. A lot of special rel. books do not cover special rel. using this mature approach, they tend to water down the math, but this book has prepared you for it so why not use it.
Also in the Special Rel. sections your Electrodynamic skills will be improved. You are now re-introduced to Maxwell's equations. You might have seen some of the mathematics before in an Electrodynamics course, but this book has given you the math skills you need to really understand it. So now you learn the tensor way to express Maxwell's equations. At this point you start feeling good about your Tensor Analysis skills. You seem to feel the whole universe coming together.
Then the moment you have been reading the book for. The author's start covering General Relativity. As you start reading this part of the book you start feeling good. You are really able to follow what is being done, because the book has done it's job and you have all the background to follow along. Then the most magic moment comes as you are shown how the metric tensor(g) is really the gravitational potential. And now it all comes together and you see how geometry plays a roll in the theory of gravity.
The rest of the book is applications of Einstein's field equations to cosmology. The book also goes into black holes. These are the hardest sections of the book but again the book does such a good job of teaching you what you need, these sections also flow.
In order to get the full benefit from this book you must go through all the steps in the book. In reality most of it is just algebra. I also recommend supplementing this book with Schaum's outline on Tensor Calculus. A lot of people way more knowledgeable in the subject than I am have also recommended this book.
Relativity Demystified is another good book, but it takes a little different approach than this book. It uses Cartan's equations to calculate the Christoffel and Ricci Tensors, but a lot can be learned from doing things a different way. The method called one-forms is really important in learning other subjects. I really recommend Relativity Demystified to get a fuller background for when you read more advanced books. It has typo's and wrong equations in it, but you can find them.
After studying these three books you will be ready to read way more advanced books. These books also give the background required to understand QFT since it requires a very good understanding of Tensors and Relativity. A lot of people have trouble with QFT not because of their Quantum Mechanics skills but because of their lack of Tensor and Relativity skills.
When you are finished you will find General Relativity is not so hard, and there are really only a few ideas behind the whole subject. I always like to supplement textbooks with at least one or two other books. Finding the books that best supplement a books is sometime hard and I have helped you with two in-expensive books.
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10 of 20 people found the following review helpful:
5.0 out of 5 stars
Tensors, Relativity, and Cosmology, First Edition by Mirjana Dalarsson ..., April 25, 2006
This review is from: Tensors, Relativity, and Cosmology (Hardcover)
An excellent introductory book to this exciting subject. Covers all neccessary calculations to master the subject easily. Strongly recommended to all students new to this subject as well as to researchers who need to refresh the technical skills in this subject.
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