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