Customer Reviews

A First Course in General Relativity

5 star:		(18)
4 star:		(9)
3 star:		(3)
2 star:		(0)
1 star:		(1)

 

 

This book is the one text I'd give to someone who aspires to learn the mathematics of general relativity. Aimed at a reader who has a grasp of three-d vector calculus and a firm basis in special relativity, this book is an ideal bridge between a text like French's "Special Relativity" and the Big Book--Misner, Thorne, and Wheeler's "Gravitation." Schutz says that his book should prepare a reader to move confidently into texts like MTW, and I think he's spot on. I'd put Rindler's "Essential Relativity" at a slightly lower level than this text. Rindler demands less of the reader going in, and probably gives more in the way of conceptual intuition regarding black holes and modern cosmological models, but Rindler doesn't leave the reader with the mathmatical understanding that Schutz does. One could stop after Rindler with a sense of having learned some things--one ends Schutz with a sense of being prepared to learn a lot more.

The first chapters refreshes the reader's mind about SR, and then proceeds to build tensor analysis in SR. What makes this book stand out it uses the language is that of modern GR--one learns the language of one-forms and vectors, not co- and contravariant vectors. Cultivating a geometrical intuition about these strange new objects (a la MTW) is given equal or greater weight than developing skills at index manipulation. Those are two reasons I'd recommend this book over Foster and Nightingale, for example. For me personally, Schutz's path toward the mathematics of curvature beginning with Cartesian and polar coordinates in 2d was easier to follow than any treatment I've seen.

Once the mathematical structure (which is the book's core) has been laid out, the physics that follows is a bit different than most texts: slightly curved spacetimes, then the field equations, and then chapters on gravitational radiation and stellar theory. I liked that. Gravitational waves are a sexy topic and an area of lively research, so putting the chapter where it is left me feeling that I'd really accomplished someting by getting that far, and had caught at least a glimpse of the frontier. The last two chapters--Schwarzchild spacetime and cosmology--are still good, but also more abbreviated; one can't fit everything in. (MTW clearly tried, and although it's the book I'd have on a desert island if I had only one GR book there, Schutz has a big edge over MTW in being portable.)

This book has a good selection of problems, with brief hints and answers. It's excellent for self study--I think actually having it as a course material with a teacher would be rapture.

A fairly complete presentation commencing with special relativity and concluding with gravitational waves and cosmology. Although intended to be used as a classroom text, the mathematically inclined reader with a firm grasp on differential equations and vector calculus can work through the text on one's own. I recommend Steven Wienberg's book GRAVITATION as a companion text for both a different perspective and to help overcome some of the conceptual hurdles.

You don't need to be satisfied with the poetry of lay books when a mathematical understanding is within your grasp!

This a very readable book that covers a lot of topics nicely. It gives a solid introduction to many of the main topics in the field. The only complaint I have is that it doesn't cover enough material.
My advice if you want a complete understanding of the field is to buy this and the Ohanian text (which is very thorough, pleasantly readable and does covering just about everything you need). Read them side by side and once that is done move on to Wald. Don't bother with MTW, its is a tome of scattered bits and pieces that work as a reference but it is NOT something from which you want to learn the subject.

This was the first book i read as an introduction to general relativity.The physical insights are truly great and the mathematics are presented in an easy to follow way needing only very few requirements.
Im writing this rewiew nevertheless to explain why i rate it with 4 stars rather than five.The preblem i believe this book has is with the philosophy that tensor calculus is analyzed.
The author begins with proving tensor calculus equation in a way that is valid ONLY for special relativity,then proceeds with the analysis of tensor calculus for the 2-d eucledian space,and again the equations are valid ONLY for the given space.
In the end the author generalises the tensor equations for any spacetime using the Equivalence Principle,and not a solid mathematical proof,whitch Ifound confusing.
As a result i give the book 4 stars because of the lack of a truly solid mathematical analysis of the manifold thery.Nevertheless its a great book for a beginner.

This book is aimed at an undergraduate/first-year graduate level, but doesn't "pull any punches" mathematically. I thought he pulled it off. The book was accessible to a non-physicist like me, while satisfying my urge to go well beyond the Scientific American level of popular science books.

After being overwhelmed by Misner, Thorne and Wheeler, I was relieved to be introduced to this fine little book that was used along with D'Inverno in my first relativity class. The accessibility of Schutz, given the advanced nature of the subject, is second to none. Each chapter includes many problems that are of a calculational nature that help you get a feel for the subject. I was really impressed with his chapters on vectors and tensors, where Schutz gives you a good feel for tensors in general and one forms in particular. His description of the covariant derivative was also very nice. Later chapters, such as cosmology and gravitational waves, didn't strike me as good as the earlier chapters. Nonetheless I definitely recommend this book to get you started with the subject.

I got to this book after I had read several GR texts.

Unfortunately, I could have saved much time and grief if I had read it first.

The author is a master in simplifying the often mystical theory of General Relativity.

One requires only a smattering of vector calculus and linear algerbra to begin.

The author begins with an review of SR followed by an introduction to tensor analysis. The notion of perfect fluids culminating in the stress energy tensor is developed.

The mathematics of curved spaces ( Riemann manifolds ) is introduced via christoffel symbols which roughly speaking tell us how the co-ordinate systems change from point to point. The covariant derivative is then introduced and it's nice properties demonstrated. Although connections are not introduced it is shown how the metric induces a natural definition of covariant derivative such that the christoffel symbols possess a certain symmetry condition. This symmetry condition is equivalent to the statement that the covariant derivative of the metric tensor be zero. Once this is achieved one can express christoffel symbols in terms of the metric components.

This is known as the Levi-cevita "connection" in other texts.

Now that we can differentiate on curves spaces ideas of parallel transport and geodesics are developed.

It is then shown that inertial observers in GR travel along geodesics.

The reimann, ricci and einstein tensors are introduced.

Now, we get to the exciting Einstein field equations. I particularly liked how the author gives the motivation and insipiration behind the equation. He shows how Newtons equation for gravitation gives the inspiration for it's generalization. We see how the stress energy tensor represents the "mass density" correlate in Newton's equation. Since this is a (2,0) tensor the left hand side of the equation must also be a ( 2,0) tensor. It is shown that the Einstein Tensor is the best fit.

Thus we see how the presence of matter ( stress energy tensor ) affects the curvature of space ( via the metric components contained within the einstein tensor ).

Now, the resulting equation is simplified to the Newtonian limit ( weak fields - minkowski space with a perturbation factor lead to linearized equations and fields to weak to produce high velocities simplifies the stress energy tensor). These are solved and yield a metric. This metric is then used to calculate the Christoffel symbols which in turn determine the geodesics and hence the motion of particles. We see that these equations of motion are exactly those predicted by Newtonian gravity.

More complicated applications to spherical stars and black holes is explored.

The book is replete with "pearls". For example the importance of the idea of tensors is repeatedly demonstrated. The author shows how tensor equations are INVARIANT under co-ordinate transformations. Thus if an equation is true in one system it is true in ALL systems. This has important applications in simplifying problems. The author does this repeatedly to draw important conclusions.

There are plenty of exercises from basic to advanced.

A first course in GR is a good read. I chose to write this review because, lately, the book has been getting bad reviews, when I think these reviewers have not put this text in perspective. There are few decent books on relativity, and this one must be one of the best. There are books on Minkowski and Schwarzchild geometry and metrics, but the actual equations of GR are being lost nowadays, and that which is lost is presented in this text in an easy to follow manner-- the actual equations not the reduction of the equations to simpler forms. I also learned the majority of my linear algebra from this book. As a whole, the book fills in the many gaps the author's of the Relativity spinoffs do not have the insight to cover. I am about to read this text for the second time in a year.

Highly recommended for anyone interested in learning the basics of one of the most important physical theories of all time.

All the key concepts in the theory are clearly explained. Some important consequences of General Relativity are covered in some detail - gravitational waves and black holes for example.

The mathematical level of detail is moderate; a knowledge of basic differential equations will get you through. The mathematical tools of General Relativity: tensors and one-forms, etc, are covered in early chapters.

Problems are provided at the end of each chapter and range in difficulty from straight mechanical computation to challenging. Solutions to selected problems are provided at the end of the book.

Schutz's book, "A First Course in General Relativity", along with J. Foster's/ J.D. Nightingale's book, "A Short Course in General Relativity", are the ones to study prior to tackling the massive (sorry about the pun) Gravitation, by MTW. The logical arrangement of relativity is much better in these books than in MTW, although MTW treats more matters more thoroughly (can't help the puns). Schutz seems more like a physicist, and Foster/Night. seem more like mathemeticians. Both viewpoints help substantially! If I were only to get one of these books, I would get Schutz's first. Then get the Foster/Night. one. For example, F/N have a better treatment of the dual basis! However, only MTW treat the convenenient non-coordinate othornormal basis!