Differential Forms and the Geometry of General Relativity
1st Edition
Published on 14. October 2024
Book
Paperback/Softback
322 pages
978-1-032-92216-4 (ISBN)
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.
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.
Reviews / Votes
"In this book, the author outlines an interesting path to relativity and shows its various stages on the way ... The author inserts suggestive pictures and images, which make the book more attractive and easier to read. The book addresses not only specialists and graduate students, but even advanced undergraduates, due to its interactive structure containing questions and answers."-Zentralblatt MATH 1315
"...the presentation is very far from the 'definition-theorem-proof-example' style of a traditional mathematics text; rather, we meet important ideas several times, and they are developed further with each new exposure. This is a pedagogical decision which seems to me to be sound, as it allows the student's understanding of the ideas to develop."
-Robert J. Low, Mathematical Reviews, June 2015
"This is a brilliant book. Dray has an extraordinary knack of conveying the key mathematics and concepts with an elegant economy that rivals the expositions of the legendary Paul Dirac. It is pure pleasure to see far-reaching results emerge effortlessly from easy-to-follow arguments, and for simple examples to morph into generalizations. It is so refreshing to find a book that does not obscure the basics with unnecessary technicalities, yet can develop sophisticated formalism from very modest mathematical investments."
-Paul Davies, Regents' Professor and Director, Beyond Center for Fundamental Concepts in Science; Co-Director, Cosmology Initiative; and Principal Investigator, Center for the Convergence of Physical Science and Cancer Biology, Arizona State University
"It took Einstein eight years to create general relativity by carefully balancing his physical intuition and the rather tedious mathematical formalism at his disposal. Tevian Dray's presentation of the geometry of general relativity in the elegant language of differential forms offers even beginners a novel and direct route to a deep understanding of the theory's core concepts and applications, from the geometry of black holes to cosmological models."
-Juergen Renn, Director, Max Planck Institute for the History of Science, Berlin
More details
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Postgraduate
Product notice
Paperback (trade)
Unsewn / adhesive bound
Illustrations
87 s/w Abbildungen
87 Illustrations, black and white
Dimensions
Height: 229 mm
Width: 150 mm
Thickness: 18 mm
Weight
522 gr
ISBN-13
978-1-032-92216-4 (9781032922164)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
10/2014
1st Edition
A K Peters
€161.50
Shipment within 15-20 days
E-Book
10/2014
1st Edition
CRC Press
€79.49
Available for download
E-Book
10/2014
1st Edition
CRC Press
€79.49
Available for download
Content
Spacetime Geometry: Spacetime. Symmetries. Schwarzschild Geometry. Rindler Geometry. Black Holes. General Relativity: Warmup. Geodesic Deviation. Einstein's Equation. Cosmological Models. Solar System Applications. Differential Forms: Calculus Revisited.