Differential Geometry and Relativity Theory: An Introduction

By R.L. Faber

Book Overview

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity

• Format: Hardcover
• Language: English
• ISBN: 082471749X
• ISBN13: 9780824717490
• Release Date: May 1983
• Publisher: CRC Press
• Length: 272 Pages
• Weight: 0.45 lbs.
• Dimensions: 0.7" x 6.3" x 9.3"

Customer Reviews

10 stars ....

I've read (attempted to read) a number of books on general relativity, including the elementary texts (Schutz, others), the introductions for mathematicians (Lee), books on tensors, web intros, .... and the only one that I've been able gain any traction with is this book. And, I'm not exactly unprepared, as I have a MS in math and have worked a number of years as an engineer, much of the time doing inertial nav and other presumably related work. Yet, the other GR books have completely baffled me. Warning ... if you start a book and there is a long section on tensors .... look out... or you'll soon be playing a game of 'find the pea (relativity)' and it will be under plenty of thick mattresses (tensor analysis being but one). This book develops all the machinery using a 2-d surface embedded in 3-d. This is the way to go, no question in my mind. There is a degree of concreteness to counter the endless poliferation of new symbols and notation. Then there is a good (could have been better see the Calculus Without Tears web page) intro to special relativity. And then .... before you've finished breakfast ... field equations... which I'm working on now. If not for this book, I might have given up on my latest hobby, GR. For example ... spacetime is curved? Yes. Hard to visualize? No. Throw a ball ... look at the arc .... there it is. Calculate the curvature? Easy... no tensors, field equations, differentials. Of course, even Faber waits till page 274 for this little demonstration, and he could have put it on page 1... still, it's there.

Highly recommended. Shame about the price

The first part of this book is a lucid introduction to classical differential geometry from the Frenet formulas to Riemannian manifolds, via Gauss curvature, metric coefficients, connections, geodesics and the curvature tensor, with many well-motivated examples and exercises. If you have a working knowledge of basic linear algebra and multivariable calculus you should have no trouble with any of this. The remainder (two-thirds of the book) provides one of the most readable introductions to special and general relativity that I have ever come across. Because of the geometric approach, modest prerequisites and limited space, there is no treatment of relativistic mechanics, electrodynamics or the 'matter' field equations, and actually no formal development of tensor calculus. Within these constraints, it is amazing what the author does manage to cover. You will be led easily through the vacuum field equations, Schwarzschild solution, perihelion precession, light-bending ...If this book had been twice the length - more comprehensive but in the same style - it could have been a classic. As it is, it does not seem to be anywhere near as widely used as it deserves to be .. Surely this is a prime candidate for a ..Dover edition? Until then, get it from the library.

A very accessible book - well worth a look

This book comprises two sections. The first section develops the tools of classical differential geometry with a thorough treatment of 2D surfaces embedded in a 3D space. First and second fundamental forms are introduced and their relationships analysed. This leads into the usual realms - Christoffel symbols, connections and the Riemann Curvature Tensor.A very readable account of Gauss's Theorem Egregium is presented - it's great!. Finally, more abstract manifolds are presented.I worked thoroughly through the first half of this book.There are many good exercises.This volume is cited a number of times In Gregory L. Naber's 'Spacetime and Singularities'- a more difficult book. I found Faber's volume of real help when studying the latter(which has loads of exercises and problems but no hints/partial solutions at all). The second section is an introduction to Special and General Relativity. I have to confess I did not study this half as I had already covered the material presented in this section elsewhere. The first half of the book gives a very good feel for curved space and is fitting preparation for the second half if the material presented there is new to you.. A good little book for independent study.