General Relativity: With Applications to Astrophysics (Theoretical and Mathematical Physics) [Hardcover]

Norbert Straumann (Author)

Book Description

ISBN-10: 3540219242 | ISBN-13: 978-3540219248 | Publication Date: July 12, 2004 | Edition: 1

The foundations are thoroughly developed together with the required mathematical background from differential geometry developed in Part III. The author also discusses the tests of general relativity in detail, including binary pulsars, with much space is devoted to the study of compact objects, especially to neutron stars and to the basic laws of black-hole physics. This well-structured text and reference enables readers to easily navigate through the various sections as best matches their backgrounds and perspectives, whether mathematical, physical or astronomical. Very applications oriented, the text includes very recent results, such as the supermassive black-hole in our galaxy and first double pulsar system

Editorial Reviews

Review

From the reviews: "In this book Norbert Straumann presents a pedagogically precise and highly informative account of both the physical and advanced mathematical concepts that a professional working in this field requires. The essential differential geometry background is placed in an extensive part … . the treatment is both physically rigorous and comprehensive. This book is an important acquisition for anyone working in this area." (Geoffrey Bicknell, Australian Physics, Vol. 42 (4), September/October, 2005) "This text provides a comprehensive and timely introduction to general relativity. … The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for strong theory and other fields of physics, classical as well as quantum." (ETDE Energy Database Energiedatenbank, November, 2004) "From the earliest sections, Straumann makes absolutely no pretence that this is a beginner’s guide to general relativity … . There are points of interest for those disinclined (or unable) to follow the maths in detail. … this book is primarily aimed at those who want to get very, very intimate with the mathematics of general relativity in an astrophysical …. context and who are endowed with a considerable background in all three subjects. … this may be the ultimate specialist textbook." (Roger Feasey, Journal of the Auckland Astronomical Society, 2005)

From the Back Cover

This text provides a comprehensive and timely introduction to general relativity. The foundations of the theory in Part I are thoroughly developed together with the required mathematical background from differential geometry in Part III. The six chapters in Part II are devoted to tests of general relativity and to many of its applications. Binary pulsars are studied in considerable detail. Much space is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and derivations of the basic laws of black hole physics. The final chapter of this part contains Witten's proof of the positive energy theorem. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for string theory and other fields of physics, classical as well as quantum.

Product Details

• Hardcover: 686 pages
• Publisher: Springer; 1 edition (July 12, 2004)
• Language: English
• ISBN-10: 3540219242
• ISBN-13: 978-3540219248
• Product Dimensions: 9.3 x 6.4 x 1.2 inches
• Shipping Weight: 2 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: #2,304,970 in Books (See Top 100 in Books)

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11 of 11 people found the following review helpful:

5.0 out of 5 stars A Masterpiece, March 4, 2008

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This review is from: General Relativity: With Applications to Astrophysics (Theoretical and Mathematical Physics) (Hardcover)

For the graduate student of physics or mathematics who has the requisite background in modern differential geometry, Straumann's text presents the most mathematically honest and thorough introduction to general relativity currently available in book form. This book is a masterpiece and belongs in the company of the classic books by Misner, Thorne and Wheeler, Penrose and Rindler, and Hawking and Ellis.

Potential readers must understand that there has been an uneasy truce between modern differential geometry and general relativity for nearly a century. While mathematicians developed the subject of Riemannian geometry along largely coordinate-free lines, reaching ever greater levels of abstraction and geometric insight, physicists continued to develop the related subject of semi-Riemannian (also called pseudo-Riemannian) geometry along coordinate-based lines, mired in complex index computations and the awkward notation that accompanies them. This is reflected in the Introduction to an excellent 1990 text on semi-Riemannian geometry in which the authors, explaining their choice of title, offer the semi-humorous lament, "Any possible title would mislead somebody. 'Tensor Analysis' suggests to a mathematician an ungeometric, manipulative debauce of indices, with tensors ill-defined as 'quantities that transform according to' unspeakable formule."

Misner, Thorne and Wheeler introduced a generation of students to the power of modern, coordinate-free methods in general relativity in the early 1970s in their classic book "Gravitation," citing the wonderful book by Bishop and Goldberg as their standard reference for semi-Riemannian geometry. Sadly, however, the modernization of the subject that MTW initiated did not seem to entirely catch on within the physics community. A number of very recent texts on general relativity have been printed in the past decade by highly reputable publishers, all written in an entirely index-based approach that was already becoming outdated and deficient over 30 years ago. The serious student of relativity already faces considerable challenges in mastering the formidable mathematical preliminaries to the subject; the work surely need not be compounded in difficulty by total reliance on obscure, unmotivated, index-based computational gymnastics. What students need is a thoroughly modern and enlightened introduction that teaches them to move comfortably and effortlessly between index-free and index-based approaches, permitting them to read and understand both the older and modern literature, both the physics and mathematical literature.

Straumann's book offers an introduction to general relativity that is completely modern in its approach to the mathematics. The final five chapters, covering roughly 100 pages, provide concise but readable introductions to basic manifold theory, Lie differentiation, differential forms and integration on manifolds, and the theory of affine connections (this latter does not provide an introduction as thorough as is found in volume 1 of Kobayashi and Nomizu---there simply is not room to study Ehresmann's approach to connections in this overview). Any student who has been fortunate enough to study the mathematical preliminaries from a modern treatment, such as Barrett O'Neill's wonderful Semi-Riemannian Geometry with Applications to Relativity, will be able to master the mathematical material in Straumann without undue stress.

One final piece of history to fully drive home the point. Richard Bishop and Barrett O'Neill introduced the notion of warped product manifolds to Riemannian geometry in the 1960s, providing one way of decomposing a manifold into two smaller and "simpler" parts. Beem and Ehrlich observed in 1982 that many of the well-known exact solutions to Einstein's equations are natural examples of warped products. The use of warped product formulas offers significant simplification of the analysis of these exact solutions. The use of warped products became central in O'Neill's 1983 book on semi-Riemannian geometry, and in Beem, Ehrlich and Easley's 1996 book on Global Lorentzian Geometry. Other authors have been slower to recognize and employ this powerful tool, and the reader will barely find warped products mentioned at all in modern texts on general relatitivy. In stark contrast, Straumann's book contains an entire section on warped products and makes full use of the simplifying formulas throughout: another sign of the progressive nature of the book.

I recommend this book in the strongest possible terms to all serious students of general relativity. If your background in differential geometry in inadequate, then I recommend purchasing O'Neill's book along with Straumann's as a packaged set. I view the O'Neill/Straumann pair as the current successors to the tradition begun by the Bishop and Goldberg/Misner, Thorne, and Wheeler books of an earlier era.

Dr. Straumann already updated this book in 2004 to a far more extensive second edition. We can only hope that as developments in our understanding of the large-scale structure of the universe progress through observational astronomy, Dr. Straumann will continue to update his book to include recent experimental and theoretical results.