Exploring Black Holes: Introduction to General Relativity [Hardcover]

Edwin F. Taylor (Author), John Archibald Wheeler (Author)

Book Description

ISBN-10: 020138423X | ISBN-13: 978-0201384239 | Publication Date: July 22, 2000 | Edition: 1

A concise, direct examination of general relativity and black holes, Exploring Black Holes provides tools that motivate tools that motivate readers to become active participants in carrying out their own investigations about curved spacetime near earth and black holes. The authors use calculus and algebra to make general relativity accessible, and use quotes from well-known personalities, including Einstein, to offer further insight. Five chapters introduce basic theory. The book also includes seven projects regarding the analysis of major applications. Discussions provide the background needed to carry out projects. The book's projects guide readers as they fill in steps, compute outcomes and carry out their own investigations. For astronomers, mathematicians and people interested in learning about the relativity of black holes.

Editorial Reviews

Review

American Journal of Physics, Vol. 69, No. 11, pp. 1212-1213, November 2001

(c)2001 American Association of Physics Teachers. All rights reserved.

Most students embarking on a major in physics probably anticipate that they will have the opportunity to elect one or more semesters of study in relativity, and many students majoring in mathematics and computer science also have a strong interest in the subject. Among the introductory texts on special relativity, Taylor and Wheeler's Spacetime Physics (SP), with its conversational tone and its emphasis on geometry, has long played an important role. However, there have been few if any books on general relativity that have managed to be both scholarly and truly introductory. Exploring Black Holes: Introduction to General Relativity (EBH) is just such a book. Through carefully chosen restrictions on coverage, the authors enable the serious study of general relativity by students who have completed a year of calculus and who are prepared for intellectual labor.

The book has been years in the making; there were several self-published preliminary versions. Thomas Roman of Central Connecticut State University provided a post-use review of the 1995 version (Scouting Black Holes: Exploring General Relativity with Calculus) in this journal [63, 1053-1054 (1995)]. EBH retains the basic structure of that earlier version, but the authors have made many improvements, additions, and corrections. The process of refinement continues: I am informed that Edwin Taylor uses each new printing of the text to correct errors and polish explanations.

I used EBH in a course entitled "Topics in Physics: Relativity" at James Madison University during the Fall 2000 semester; the prerequisites were one year each of physics and calculus. Fourteen students enrolled for the course, and twelve completed it (six seniors, three juniors, and three sophomores). All had encountered special relativity in the introductory physics survey, and the upper-division physics majors had also spent a couple of weeks studying special relativity in a one-semester modern physics course.

EBH was one of three required texts, the other two being SP and Kip Thorne's Black Holes and Time Warps (a narrative of the development of general relativity as witnessed by one of its foremost practitioners). Approximately half of the semester was devoted to a thorough discussion of special relativity using SP. The first few chapters of Thorne's book were
also assigned in the first half of the semester, both to lighten the reading load during the second half and to accustom students to Einstein's geometrical vision of gravitation.

During the eight weeks devoted to general relativity, the class managed to cover all five chapters of EBH (Speeding, Curving, Plunging, Orbiting, and Seeing) and four of the seven "projects." Students found the project on the Global Positioning System (GPS) fascinating, both because several of them had used GPS devices and because general-relativistic effects must be included in the analysis in order to for the GPS system to be accurate enough to be useful.

Almost without exception, the students rated EBH as very clear and interestingly written. Their previous contact with GR (if any) was of the "gee-whiz" variety, and they took evident pride in being able to grapple with some of the intellectual challenges of the theory. The authors are careful to acknowledge the limitations of a treatment in which the mathematical apparatus is limited to a year of calculus, but the students and I were pleased at how much can be accomplished. Our experience suggests that any physics professor who is prepared to make the effort can provide a worthy undergraduate introduction to GR, with the help of Taylor and Wheeler. My only prior experience with general relativity was a two-semester sequence (based on Weinberg's Gravitation and Cosmology) taken as a graduate student many years ago.

The black and white text is replete with sample problems, well-drawn and amply captioned figures, and a good collection of end-of-chapter exercises. One idiosyncrasy that several students found annoying is that each chapter and project has its pages independently numbered. Because the chapters are identified by numbers and the projects are identified by capital letters, it is not always clear which way to turn when searching for a particular passage.

Using EBH may also require an adjustment by those physics students and teachers who have come to expect that all physics texts should have a high ratio of equations to explanatory sentences. But the prose of this text is rich, sometimes whimsical, and always aimed directly at helping the reader develop an intuition for the physics that lives beneath the mathematical surface.

Spacetime Physics is a jewel of an unconventional book on special relativity. With Exploring Black Holes, Taylor and Wheeler have presented the community of physics learners and teachers with another gem.

VITAE

William H. Ingham is Professor of Physics at James Madison University. His interests include astrophysics, computational fluid dynamics, and thehistory of science.

From the Back Cover

A concise, direct examination of general relativity and black holes, Exploring Black Holes provides tools that motivate tools that motivate readers to become active participants in carrying out their own investigations about curved spacetime near earth and black holes. The authors use calculus and algebra to make general relativity accessible, and use quotes from well-known personalities, including Einstein, to offer further insight. Five chapters introduce basic theory. The book also includes seven projects regarding the analysis of major applications. Discussions provide the background needed to carry out projects. The book's projects guide readers as they fill in steps, compute outcomes and carry out their own investigations. For astronomers, mathematicians and people interested in learning about the relativity of black holes.

See all Editorial Reviews

Product Details

• Hardcover: 352 pages
• Publisher: Addison Wesley Longman; 1 edition (July 22, 2000)
• Language: English
• ISBN-10: 020138423X
• ISBN-13: 978-0201384239
• Product Dimensions: 10 x 8.2 x 1.2 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #144,167 in Books (See Top 100 in Books)
  • #53 in Books > Professional & Technical > Professional Science > Physics > Relativity

Customer Reviews

Most Helpful Customer Reviews

42 of 44 people found the following review helpful:

5.0 out of 5 stars Dear Prospective Students of General Relativity., August 23, 2000

By 

Bruce Pew (Oceanside, Californis USA) - See all my reviews

This review is from: Exploring Black Holes: Introduction to General Relativity (Hardcover)

'Exploring Black Holes' was meant for me. I'm 54 years old andhave spent the last 3 years learning some mathematics with a goal of learning more than just the concepts of General Relativity. My math skills leave me in the group Professors Edwin F. Taylor and John Archibald Wheeler are trying to reach with 'Exploring Black Holes'. The purpose behind Professors Taylor and Wheeler writing the book is explicitly stated in the 'The Author, Edwin F. Taylor' and 'Back Cover Copy' sections for 'Exploring Black Holes' located at Amazon.com. My purpose in writing this review is to point out that 'Exploring Black Holes' is not just for university students but is also a very effective tool which can be used for 'self study'. Used by folks such as myself. Terms and methods are clearly defined eliminating the need to search for explanations outside the text of 'Exploring Black Holes'. Step by step example problems are provided to insure problem solving can be achieved through self study and the text is 'fun' to read...I sincerely recommend 'Exploring Black Holes' as a self study introduction to General Relativity and I would like to thank Professors Taylor and Wheeler for making this unique approach available. Sincerely Yours Bruce Pew

40 of 42 people found the following review helpful:

5.0 out of 5 stars Just wonderful!, April 10, 2002

By 

henrique fleming - See all my reviews

This review is from: Exploring Black Holes: Introduction to General Relativity (Hardcover)

This book is different from every other introduction to general relativity I know. And better. The eminent authors connect geometry directly to physics, bypassing tensors. Curvature in space is detected by very simple length measurements; curvature in time, by the lengthening of periods of oscillations. There are nuggets in almost every page. I loved the demonstration that you don't really need coordinates to describe geometry: the shape of a boat is reconstructed entirely in terms of distances. Their dynamical principle is the maximum proper time principle. The way they derive energy and momentum from this principle is sterling physics. You'll learn a lot of general relativity in this book. Not all of it. But, learning to love it, you'll learn the advanced topics that cannot be treated this way by yourself, in other books. Perhaps in the huge Misner, Thorne, Wheeler.

31 of 32 people found the following review helpful:

4.0 out of 5 stars teaches calculations, some statements without justification, January 13, 2005

By 

smallphi (Chicago, IL) - See all my reviews

This review is from: Exploring Black Holes: Introduction to General Relativity (Hardcover)

I am a graduate student in physics and I like reading books for undergraduates like this one. I've learned more from this book than from the 'bible' MTW or from the usual superficial graduate courses in GR that boil down to 'index gymnastics' whithout conceptual depth.

The dominant theme in the book is spherically symmetric noncharged and nonrotating black holes described by the Schwartzschild metric. Only the last two projects deal with rotating black holes and cosmological metrics. The book covers only a small application chapter of GR so don't expect to see the Einstein equations or tensors (there isn't a single one).

It took me a month to read the book and do all the exercises which I found easy most of the time since they come with pretty detailed instructions how to solve them. You will need to know a little special relativity and calculus so it is completely within the reach of an undergrad. Also the authors prefer to work directly with the differentials in the metric instead of using 4-vectors, scalar producst and components - that is more natural for most beginners. You can see the 4-vector approach in more advanced books (still for beginners) like James Hartle's "Introduction to general relativity".

The Schwartzschild metric is stated without derivation. Then you are introduced to 3 different observers around the black hole and their measurements. You will use a variational principle called in the book 'Principle of extremal aging', to derive the orbits of bodies and light rays around the black hole and constants of motion like energy and angular momentum. The radial motion is tackled through 'effective potential', the angular motion through the angular momentum.

At the end of the book you will begin to understand how to tackle a general metric: how to interpret its coordinates in terms of measurements performed by different observers, how the constants of motions are connected to symmetries in the metric, how to get the constants of motion with the variational principle and so on...

Besides all that, you will learn a bunch of wonderfull facts about black holes that will make you a star at a nerd's party :) Can you cross the horizon and what is seen by different observers, the time from the moment your body feels uncomfortable till the moment you reach the center of the black hole, how the night sky looks close to the black hole and so on.

Some of the projects in the book calculate the hystorical experimental proofs of GR: bending of light near sun, precession of mercury's orbit and so on. The projects contain queries that you have to fill in reading the text. The solutions of these are usually shorter than the questions themselves :)

My only objection is that sometimes the book makes statements without justification. For example, it is enogh to say that the principle of extremal aging like every principle is a statement in agreement with the experiment that can't be proven, we just know it works but don't know why. Instead of explaining that, the book states the principle several times wasting paper to my opinion and you still don't understand where that principle comes from. Repeating statements without proper explanation is equivalent to brain-washing and just makes the text unnecessary bulky and inefficient.

UPDATE for the authors [6 Nov 2007]: What I meant with the above paragraph is that while the 'principle of extremal aging' can be shown to follow from the assumptions/axioms in the context of Special Relativity (like in the twin paradox), in GR it is postulated by analogy, not proven. Sections 3.1 and 3.2 illustrate the principle but are not explicit enough about its origin in GR.

For sins like that I gave it 4/5. Keep in mind I am a pretty demanding reader and I give 5/5 only to masterpieces like some books of David Griffiths where you can see the authour applied great effort to streamline the logic and clearly justify it to the reader.