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Relativity on Curved Manifolds (Cambridge Monographs on Mathematical Physics) 1st Edition

5 out of 5 stars 1 customer review
ISBN-13: 978-0521266390
ISBN-10: 0521266394
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Editorial Reviews

Review

"This excellent monograph describes in detail the mathematical structure of Einstein's general theory of relativity, and the mathematical techniques that are associated with it. It is a completely self-contained exposition, which collects many important general results relating to the classical theory that are not readily available in the literature. It will be of great value to anyone who is already familiar with the theory, and who requires a deeper technical knowledge than is presented in most current textbooks." Mathematical Reviews

"...the authors present a book on general relativity which, on one hand, is mathematically rigorous and, on the other hand, contains good physics by emphasizing what is measurable on curved manifolds. Even those readers who are interested in more applications, such as e.g. gravitational lensing, can find all the tools necessary in this book even though this item cannot be found in the index. Thus the book can strongly be recommended to mathematicians and physicists as well." Classical and Quantum Gravity

"This is an excellent book and admirably lives up to the promise implied in its title in giving a thorough treatment of the mathematical structure underlying the theory of general relativity." The Observatory

"...a valuable reference work, particularly for its mathematical introduction and its treatment of the other topics mentioned above." Robert M. Wald, Foundations of Physics

"...provides more in details in various formalisms than do many comparable relativity books. It should prove to be a very good supplementary book for a graduate course on general relativity, or it might serve as a reference book for researchers..." K.K. Lee, Physics in Canada

Book Description

The power of the theory of general relativity cannot be exploited fully without a detailed knowledge of its mathematical structure. This self-contained exposition emphasizes tetrad and spinor structures and physical measurements on curved manifolds.
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Product Details

  • Series: Cambridge Monographs on Mathematical Physics
  • Hardcover: 464 pages
  • Publisher: Cambridge University Press; 1 edition (May 25, 1990)
  • Language: English
  • ISBN-10: 0521266394
  • ISBN-13: 978-0521266390
  • Product Dimensions: 6 x 1.2 x 9 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #5,813,043 in Books (See Top 100 in Books)

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By G. A. Schoenagel on January 12, 2014
Format: Paperback
Somewhat sophisticated monograph detailing the mathematical structures underlying Relativity. However, the exposition,
both from a mathematical and physical perspective, is crisp, lucid and innovative. (The editorial accolades are spot on).
This is not intended as a first (elementary ) textbook on General Relativity (as in, for example, Hartle ),
nor is it as massive or extensive as the inevitable classic Gravitation ( Misner, Thorne, Wheeler).
However, the text does provide a unique outlook on the differential structures central to Relativistic Physics.
The zeroeth chapter provides quick summary of the trilogy: local, global and infinitesimal as they pertain to general relativity.
Chapter One: an insightful excursion through the terrains of topology and tensors, culminating with exterior forms.
Second: Differentiation (Tensor Fields, Lie Derivatives, Exterior Derivatives), nicely accomplished.
Third: Curvature (Riemann, Ricci, Weyl, Bianchi ) Exceptional expositions, all.
Preliminaries out of the way, the real fun begins:
Tetrads and Spinors, comprising the following two chapters, are absolutely essential and delightful.
After which, the full richness of this text unfolds: Field Equations, Geometry, Conservation Laws and Congruences;
"these describe in most cases the space-time evolution of physical systems." (Page 250). In fact, Chapter Eight, Geometry
of Congruences, is one of the finest expositions to touch upon Tetrads, Null-Rays, Raychaudhuri Equation and Singularities.
Physical Measurements (Chapter Nine: "we shall apply...to...mechanics, electrodynamics, and fluid dynamics...")
and finally Spherically (Schwarzschild) and Axially (Kerr) Symmetric Solutions . Much detail , lucidly presented.
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