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Who Was Hermann Weyl?

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Weyl's Spinor and Dirac's Equation
Weyl's Conformal Tensor
Weyl Conformal Gravity
Weyl's 1918 Theory
Weyl's 1918 Theory Revisited
Weyl v. Schrodinger
Why Did Weyl's Theory Fail?
Did Weyl Screw Up?
Weyl and the Aharonov-Bohm Effect
The Bianchi Identities in Weyl Space
Conformal, Parameter-Free Riemannian Gravity
Gravity Wave Tutorial
Conformal Kerr-de Sitter Gravity
A Child's Guide to Spinors
Levi-Civita Rhymes with Lolita
Weyl's Scale Factor
Weyl's Spin Connection
Weyl and Higgs Theory
Weyl & Schrodinger - Two Geometries
Lorentz Transformation of Weyl Spinors
Riemannian Vectors in Weyl Space
Introduction to Quantum Field Theory
A Children's Primer on Quantum Entanglement
Veblen and Weyl
Graphing the Lorentz Transformation
FLRW in de Sitter Spacetime
FLRW with a Constant Curvature Scalar
Is There a Flaw in the FLRW Metric?
On the Mannheim-Kazanas Spacetime
Electron Spin
Clebsch-Gordan Calculator
Bell's Inequality
The Four-Frequency of Light
There Must Be a Magnetic Field!
Non-Metricity and the RC Tensor
Curvature Tensor Components
Kaluza-Klein Theory
The Divergence Myth in Gauss-Bonnet Gravity
Schrodinger Geometry
A Brief Look at Gaussian Integrals
Differential Forms for Physics Students
Particle Chart
Einstein's 1931 Pasadena Home Today

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Visitors since 11-4-2004:

Introduction to General Relativity
Ronald Adler, Maurice Bazin, Menahem Schiffer
McGraw-Hill, Second Edition, 1975

This is an introductory book suitable for advanced undergraduate/beginning graduate study. Tensor analysis is covered adequately, along with affine and Riemannian spaces, the gravitational equations in free space, the Schwarzschild and Kerr solutions (static and rotating black holes), descriptive astronomy, standard cosmological models, and several unified field theories, including Weyl's 1918 theory.

Although the presentation of tensor calculus is relatively elementary and in the old style (and there's not much on special relativity), in my opinion this is the best book on introductory general relativity available. In fact, it's my favorite physics text, and I have learned more from it than just about any other book on the subject. However, it desperately needs to be updated. So many discoveries have been made since the 1975 edition came out that it really looks dated (the first edition appeared in 1965, and it's worse), although the same criticism can be made to a lesser extent about Misner-Thorne-Wheeler's Gravitation (1973 edition). 

The book is extremely easy to read, and the subjects are presented in a logical sequence, culminating with the usual cosmological applications. There are relatively few exercises and problems, but the book is more a self-study resource than a textbook, anyway. While the consequences of Kerr black holes are covered adequately for an introductory text, the book predates topics such as Hawking radiation, the entropy of black holes, and the cosmic microwave background.

The last chapter is entitled Electromagnetism and General Relativity, but the authors pretty much avoid promoting the topic as unified field theory. The field of a charged mass point is treated, along with the so-called "already unified" theory of Rainer, Misner and Wheeler. The book's treatment of this theory is both interesting and comprehensible; if you've ever read any of these authors' more advanced books (or tried to), you'll appreciate this.

Interestingly, Adler et al. cannot hide a certain fondness (if that's the right word) for Weyl's 1918 theory ("a suggestive formalism that may still have the germs of a future fruitful theory"), although only 17 pages are devoted to it. The treatment is fairly elementary, but the gist of what Weyl was attempting to do is clear. Since I talk about the theory in great detail elsewhere on this site, I won't go into it any further here. 

I've seen this book advertised at Amazon, but the price is rather steep, in my opinion. eBay occasionally auctions the book at reasonable prices. If you can find one in good condition, it's a worthwhile acquisition.

By the way, Dover offers a great little reprint of a book entitled The Principle of Relativity, which is a collection of eleven old (very old!) papers on general relativity by Einstein and others, including Weyl's original 1918 paper describing his gauge-invariant unification of electromagnetism and gravitation.


As it is unlikely that the Adler-Bazin-Schiffer book will ever be updated, I am now recommending Lewis H. Ryder's text, also titled Introduction to General Relativity (Cambridge University Press, 2009). It is written at about the same mathematical level as the Adler book (beginning graduate), but includes treatments of many more recent developments and advancements in general relativity. As of 26 June 2010, the book was available from Amazon.com for about $45. I highly recommend it.