Differential Forms and the Geometry of General Relativity 1st Edition by Tevian Dray (PDF)

Description

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.The book contains two intertwined but distinct halves.Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of “index gymnastics” as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Professor Dray’s book on Special Relativity is a gem, an unsurpassed book, and should be of universal interest. This book is very good, but represents an extreme compromise. It is, I think, a compromise in the direction that most editors would most enjoy. The book itself consists of two parts, a part on the physics of relativity, and a part on the differential geometry—via differential forms—that is needed. As the book is bound, the mathematics most needed appears at the second half so that a reader can jump directly to the “good stuff” (physics) at Chapter 1. This is done even though a reasonably thorough knowledge of the mathematics is really needed for a proper understanding, and the professor’s own students usually study the material in the opposite order (for very good reason).The treatment of differential forms is very terse but pedagogical. He tells you not only the formalism but (more or less) what it means. It allows a quick understanding of “what” and “what to do,” although a deeper understanding of why it is this way could hardly be extracted by a beginning student. Here, Professor Dray is not entirely to blame. Very many authors of differential geometry are so caught up in the most rigid formalism that they seldom explain what it really means. They perfect the formalism while neglecting real understanding. This book would be ideal indeed for a poor overwhelmed student facing the material for the first time, a person who simply wanted to remain academically solvent. For others, who have both more time and greater needs, it would be much better to learn differential forms from Shigeyuki Morita’s book or even from Bott and Tu. The “real” course in differential geometry is Barrett O’Neill’s book on Semi-Riemannian Geometry. It is understandable, although not committed as much to differential forms and somewhat more formal. Real understanding of differential forms is more accessible with Morita.For the relativity part, Professor Dray gives very good insights, and there is no reason to criticize him. For me, Oyvind Gron’s books are better for the “kinder, gentler” introduction to general relativity because they give a more complete picture and include reasonably deep results. There is no replacement for Wald’s book or even the telephone book of Misner, Thorne, and Wheeler, although it is almost time to update it. Professor Dray’s book on General Relativity is probably the best true crash course available anywhere. For those who are not actually crashing, I think other, somewhat longer introductions will give more insight.

⭐As a textbook, or for self-study, the book is woefully inadequate. It is too disorganized, leaves out too many steps and interconnecting material, and is occasionally incomprehensible. The first five chapters, though, are quite nifty if you just accept the solutions (metrics) and jump in. You’ll get to things like circular photon orbits around black holes and the precession of Mercury’s orbit extremely fast without mountains of differential geometry. It reads like a tasting menu, and for Chapters 1-5 that formula works reasonably well, if you’re willing to take Appendix A (and a few other things) on faith. Beyond that, it doesn’t serve much purpose.

⭐The book guide you from the very beginning to more advanced topics in a very didactic way. Need an annex showing the problems’ solutions. In general is good.

⭐This purchase was another attempt to find an accessible introduction to differential forms, and it actually delivered! It gave a very clear picture of how this formalism extends and clarifies the notions of classical vector calculus. The writing is clear and the notation is very clean and economical.

⭐A wonderful addition to any library wanting a differential geometry book and general relativity notes from simple ideas to more advanced topics, from scratch…It is written even for any with a minimal mathematical background. I really love it…

⭐A nice easy read. Clear and understandable.

⭐This is an excellent book with lots of good examples. which are hard to find from other higher level books. However, one star to knock off since there are some hands wavings for some concepts. Like “Differential Forms are integrands, the things one integrates” when first introducing differential forms in the book. I think this is confusing and does not really say anything. Therefore one needs another more rigid book as companion when learning the subject.

⭐Another good and useful but brief and “simple” book that I bought recently. At 85, I find it difficult to cope with very heavy and verbose tomes of 600 to 900 pages (with one or two exception). After all, the books on quantum mechanics by Dirac (pioneering) and, more recently, Weinberg are fairly brief, yet manage to contain all the essentials and more some; Einstein is probably the leader of the pack in this regard. Tevian Dray’s book sets a good, modern example.

⭐El estudio de las tres formas de la geometría diferencial está muy bien desarrolladoThis text is very poorly written. I tried twice to get through the Differential Forms section and once to get through the General Relativity section and was baffled by the lack of organization, departure from notational standards and incorrect statements (like stating that the equation for the line element “is” the metric).

⭐微分形式を使って一般相対論を解説する教科書のように見えますが，そうではありません。微分形式を大雑把に解説してから一般相対論を解説して，その後に微分形式をちゃんと解説します。そこら辺で訳がわからないのですが，後半部のホッジのスター作用素の定義もいい加減で，初学者にとっては非常に辛い内容です。難しくてもいいので，真面目に解説してくれる方がよかったように思いました。

⭐

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