Customer Reviews

General Relativity (Springer Undergraduate Mathematics Series)

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

 

 

I really like N. M. J. Woodhouse's two books on relativity: General Relativity (Springer Undergraduate Mathematics Series) and Special Relativity (Springer Undergraduate Mathematics Series) (Volume 0). They're both short, well organized, exceptionally clear and mathematically impeccable. Woodhouse is a very gifted writer: he knows how to get to the point!

Even though the book is short and mathematically oriented, it does not shirk physics motivation, as you can see via the Look Inside this Book function. Woodhouse manages to cover the basic or essential aspects of many key topics in just 178 pp. For example, Einstein's Equation is introduced and discussed in chapter 6 (pp. 89 - 94); the curvature tensor is discussed on pp. 96-98 and Killing Vectors on pp. 102-104. Other chapters deal with Spherical Symmetry, Orbits in Schwarzschild Space-time, Black Holes, Rotating Bodies, Gravitational Waves, Redshift.

Fast pace, yes; but he makes every word, definition, equation and theorem count! Anyone, like me, who has been frustrated by the many introductory general relativity books that are either confusing -- mathematically or otherwise -- or else just too detailed (I love GR but am not gonna become a physicist :), should find this new (2007) introductory book a "breath of fresh air".

Be forewarned though that they're written for senior math majors and so not suitable for anyone whose math skills are sub-par. But if your math skills are honed, both books are really a pleasure to read, especially compared to the mathematically inadequate, long-winded and sometimes downright confusing expositions of many other books.

Also, in some places I think the book is too terse, and because of this, is best used as a supplement to a book providing more complete details on certain key topics, e.g., Christoffel symbols, parallel transport, covariant derivatives, and Riemann tensor (curvature tensor).

Because of these limitations, I have taken away one star, hence the 4 star total.

[If your special relativity isn't up to par, I also recommend his book Special Relativity (Springer Undergraduate Mathematics Series) (Volume 0) as a "prequel".]

This book has its origins in a careful course on general relativity given at Oxford University. Practically speaking, it would be very reasonable to regard the volume "Special Relativity" by the same author as a prerequisite for a proper reading of this text. It gives a complete and very concise explanation, introducing the reader to "real" general relativity and not to some watered down version made for mass consumption. It makes general relativity as simple as possible, but not simpler. Because it is concise, it cannot cover all the topics readers will eventually want to explore. The textbook "Gravitation" by Misner, Thorne, and Wheeler (MTW) is truly voluminous and is itself an indispensable part of the professional literature. Woodhouse's book is a much more direct and potentially much less confusing place to begin. Wald's famous text is probably the best graduate text. Again, Woodhouse is a kinder, gentler introduction, and gives more direct intuition. With Woodhouse, you can easily notice that a geodesic is just the solution to Lagrange's equation with a null potential. That makes sense directly, physically. We can "see" that or "feel" it (if a particle isn't acted on by a force, it goes as straight as it can). In Wald's text, you get the geodesic equation and you get to form your intuition as you can. MTW tries to give more explanation, but nothing about it is really concise. One gains understanding, but it is gained slowly. Confidence also comes slowly. Woodhouse gives students a real leg up. Isn't that what University is supposed to be for---teaching something????? Not every university feels that way. At least one famous professor told me "we're not here to TEACH---our purpose is to EXPOSE MATERIAL." Of course, I held that professor in very low esteem indeed. Woodhouse is not like that. His book is a treasure, a gem. No one should be without it.