A First Course in General Relativity

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.


Solid start but you'll need Ohanian/wald   October 26, 2003
33 out of 34 found this review helpful

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.


a good solid read   June 5, 2001
17 out of 17 found this review helpful

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.


Good intro for dilettante   October 14, 1995
21 out of 22 found this review helpful

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.


Should have been my first GR book!   June 13, 2006
Rehan Dost (Canada)
20 out of 22 found this review helpful

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.