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The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics) [Paperback]

Stephen W. Hawking , G. F. R. Ellis , P. V. Landshoff , D. R. Nelson , D. W. Sciama , S. Weinberg
4.6 out of 5 stars  See all reviews (5 customer reviews)

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Book Description

March 28, 1975 0521099064 978-0521099066
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.

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Editorial Reviews

Review

"...an excellent set of reviews of some of the most exciting areas of research in gravitational physics...I have not found a comparable compilation of valuable information on the current status of general relativity." American Scientist

Book Description

This 1973 book discusses Einstein's General Theory of Relativity and its two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself.

Product Details

  • Series: Cambridge Monographs on Mathematical Physics
  • Paperback: 404 pages
  • Publisher: Cambridge University Press (March 28, 1975)
  • Language: English
  • ISBN-10: 0521099064
  • ISBN-13: 978-0521099066
  • Product Dimensions: 0.8 x 5.9 x 8.8 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #365,120 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews
36 of 37 people found the following review helpful
5.0 out of 5 stars A classic in mathematical general relativity January 17, 2002
Format:Paperback
This book is now a classic and is written by two giants in mathematics and physics. It wil be used for many years to come and is certainly one of the most widely quoted in the subject.
The authors begin the book by a discussion of the role of gravity in physics and its role as determining the causal structure of the universe. They introduce the idea of a closed trapped surface, setting the stage for the goal of the book, namely the study of the conditions under which a space-time singularity must occur. Black holes and the beginning of the universe are cited as examples of these singularities. The authors also outline briefly the content of each chapter. A neat argument is given for the significance of focal points via the use of Raychaudhari's equation.
The second chapter is an overview of the background in differential geometry needed in the rest of the book. Although complete from an axiomatic point of view, the approach is much too formal for readers who do not have a knowledge of differential geometry. Such a reader should gain the necessary background elsewhere.
General relativity as a theory of gravitation is discussed in chapter 3. Spacetime is assumed to be a connected 4-dimensional smooth manifold on which is defined a Lorentz metric. The topology is assumed to be Hausdorff. Some of the more interesting or well-written parts of this chapter include the example of a spacetime that is not inextendible, the determination of the conformal factor for the spacetime metric, and the discussion of alternative field equations.
The authors discuss the physicial significance of curvature in chapter 4, namely its effect on families of timelike and null curves.
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19 of 21 people found the following review helpful
By TAM
Format:Paperback
The early seventies saw a revolution in cosmology; for the first time, modern mathematical methods were applied to the discipline, with intriguing results. This book was (along with Penrose's articles) the seminal work in global general relativity. Often overlooked is that the first half of Hawking & Ellis is devoted to traditional GR via the tensor calculus, and the q-form conception. However, trying to learn GR with this volume is not recommended (instead, cf. D'Inverno). The meat-and-potatoes of the book is the discussion of gravitational collapse, and the singularity theorems. They provide us with intuitively good reasons for believing in some very strange phenomenon. If you're interested in the frontiers of modern science, and have the appropriate mathematical background, this book cannot be recommended too highly. The little yellow book stands supreme in the hierarchy of works of modern physics.
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25 of 30 people found the following review helpful
5.0 out of 5 stars The best book on modern General Relativity July 17, 1998
Format:Paperback
This book of Stephen Hawking is the more elegant one on modern General Relativity and is my favorite book. It covers in brilliant form the gravitational collapse of a star, the theory of black holes, the space-time singularities, the causal structure of space-time, and in its end the initial singularity of the universe, popularly known as the Big Bang. The book is highly mathematical, and is pressuposed that the reader have studied basic abstract algebra and point set topology. But, for the readers highly interested in these subjects(as I am), this is not a obstacle. All theoretical physicists interested in modern General Relativity should have this book, a testimony of the Genius of Stephen Hawking. Definitively, a magnific book.
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30 of 81 people found the following review helpful
3.0 out of 5 stars Suitable only for mathematicians October 21, 1999
Format:Paperback
Don't be mislead by Hawking's popular works, this is a book by a mathematician written for mathematicians. Unless you studied mathematics to at least graduate level (you need to understand vector calculus, vector spaces and tensors to get anywhere) you are unlikely to get much from this book. Even then to read it at anything other than the most superficial level is very hard work. However even at the superficial level it gives one insights into some interesting aspects of general relativity.
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6 of 47 people found the following review helpful
A Kid's Review
Format:Paperback
I think that this book has great depth, and is one of the best Stephen Hawking books I have read. My favourite remains 'A Brief History of Time', but still this book is extremely excellent. My compliments to the chef.
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