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General Relativity: A Geometric Approach, by Malcolm Ludvigsen
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Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.
- Sales Rank: #2356611 in Books
- Brand: Brand: Cambridge University Press
- Published on: 1999-05-28
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .71" w x 6.85" l, 1.11 pounds
- Binding: Paperback
- 230 pages
- Used Book in Good Condition
Review
"This short, elegant book describes the major ideas of special and general relativity with unprecedented clarity and mathematical depth.... Ludvigsen's book is a very good addition to the library of anyone who is interested in general relativity, black holes, and cosmology. Many who learned or studied general relativity from other sources would gain from the depth and beauty of the geometrical approach so beautifully described here." Physics Today
"A valuable effort has been made towards keeping mathematical language and machinery as simple as possible, always introducing the mathematical tools required at each step. On the other hand, all physical assumptions are clearly spelled out and their translation into mathematics is carefully made..." Mathematical Reviews
"Ludvigsen's book provides us with an elegant modern introduction to Einstein's general relativity; it is comprehensive, brief and very readable." Professor Sir Roger Penrose, Mathematical Institute, University of Oxford
"...a clear, clean, concise introduction to mathematical general relativity. It is a pleasure to see so many important topics discussed with such economy and care." Professor Bernard F. Schutz, Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Potsdam
"Ludvigsen's textbook is almost unique in its emphasis on the geometrical foundations of the theory...a refreshing and intriguing review of the subject." Dr. John Stewart, Department of Applied Mathematics and Theoretical Physics, University of Cambridge
"...a simple and elegant introduction to the subject...written in a pleasant style, with some humor, which makes it quite readable for the properly prepared student...a welcome addition to the literature." American Journal of Physics
Most helpful customer reviews
17 of 17 people found the following review helpful.
Useful, but with a STEEP learning curve
By physics student
I have taught electromagnetism at the advanced graduate level, and am reasonably familiar with classical differential geometry and general relativity (e.g. as presented by Weinberg). I am finding Ludvigsen's book a tough read, though a worthwhile one. A considerable amount both of the physics background and the mathematics background of the subject is omitted or treated very briefly. Three paragraphs cover the Coulomb potential *and* the plane wave, for instance. Definitions tend to be ostentive - by example.
Ludvigsen's book has the virtues of brevity as well as its difficulties, however: the reader can see where he is going at all times, and the author takes the reader through the modern approach to differential geometry, and deeply into the results of relativity theory, quickly and efficiently.
I hope to see a second edition of this book. A little more explanantion, here and there, would do much, if not to reduce the steepness of the learning curve, at least to provide a few handholds on the way up!
9 of 9 people found the following review helpful.
Dense
By S. Matthews
There are endorsements on the back of this from Roger Penrose and Bernhard Schutz. The two neatly parenthesise the problem with this book, which is that in order to follow it, you need first to read Schutz's 'Geometrical methods', but once you have read Schulz you can skip Ludwigsen, and have a crack at Penrose (or, more reasonably, Wald) instead.
This should be a nice book (and Roger's blurb is probably earned - but Rog is not the audience). The author is enchanted - understandably - by the beauty of both relativity and differential geometry, but he tries to do too much in the number of pages he has, forgetting that mathematical ladders are much less intimidating looking down than looking up.
A book twice as long would take half the time to read.
5 of 5 people found the following review helpful.
A good book (in particular, for students)
By Nikolai Mitskievich
This is a good book, with a pronounced mathematical accent and many useful and solvable problems. It can be considered as a textbook, though there are some points which deserve corrections, for example: (a) In p. 36, the Author characterized the Lorentz transformation too shortly, and he calls it "Lorenz transformation". This is especially strange since in the neighbouring Denmark (Ludvigsen's address in the book is in Sweden) there was a great physicist L.V. Lorenz, 1829-1891, inventor of the Lorenz condition, creator of the electromagnetic theory of light (1867, independently of Maxwell), and co-author of the famous Lorenz-Lorentz formula -- together with H.A. Lorentz of Holland to whom pertains the above transformation. Eight lines below Ludvigsen introduces "Levi-Cevita" tensor (named after T. Levi-Civita, and this is a pseudo-tensor = axial tensor). These errors are not misprints (see Index, p. 216, and the text in the pages given there). (b) The Author uses, of course, real coordinates (not the ancient imaginary time), so it is inadequate to picture the Lorentz transformation as a sheer trigonometric rotation of space-time axes (cf. figs. 4.7, 5.3). (c) In the very title of the book the subtitle ("A Geometric Approach") seems to be artificial since general relativity practically is a synonym of geometry: the well-proportioned abundance of figures in the book is not identical to geometry. Imagine that Euclid would entitle his books as "The Elements. A Geometric Approach"... But the book by Ludvigsen is definitely a success, though it needs some editing more. I highly recommend it to students.
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