A General Relativity Workbook,

Albert Einstein’s theory of general relativity leads to such spectacular predictions as black holes, gravitational waves, and the Big Bang in the early universe, all of which are at the forefront of theoretical and observational physics. Thomas Moore’s recent text, *A General Relativity Workbook*, provides an excellent introduction to general relativity and its fascinating implications for cosmology, black hole physics, and gravitational waves. A professor of physics at Pomona College in California, Moore has mainly focused his research on the generation and detection of gravitational waves. He has also authored *A Traveler’s Guide to Spacetime: An Introduction to the Special Theory of Relativity* (McGraw-Hill, 1995) and the six-volume text *Six Ideas That Shaped Physics* (McGraw-Hill, 2002).

*A General Relativity Workbook* is ideally suited for a one-semester, undergraduate-level introductory course in general relativity. The book assumes only a basic knowledge of calculus, classical mechanics, and electromagnetism, and does not require prior knowledge of differential geometry or tensor calculus. Each of the 39 chapters corresponds to a 50-minute class section, which makes it particularly handy for use as a textbook.

After a brief introduction of the principal ideas behind general relativity, the book presents a review of special relativity, followed by five chapters in which tensor fields and the index notation are introduced and explained in detail and Maxwell’s equations in tensor form are derived. Next is a discussion, based on a variational principle, of spacetime geodesics. With those concepts in hand, the reader is already capable of diving into the next eight chapters and understanding the most important physical properties of the Schwarzschild metric. Those chapters include a nice discussion on particle and photon orbits and their applications to the perihelion precession of Mercury and gravitational lensing, a demonstration that the Schwarzschild metric describes a black hole, and some heuristic comments on black hole thermodynamics.

Later chapters are devoted to the definition of curvature (based on the relativistic interpretation of tidal forces through geodesic deviation) and to a discussion of Einstein’s field equations, including a derivation of the Schwarzschild solution. The book culminates with three independent sections on main applications of general relativity: six chapters on cosmology, five on gravitational waves, and five on spinning black holes.

A novel aspect of *A General Relativity Workbook* is its overview-and-box layout: Each chapter contains a clear motivation, an overview of the key concepts and results, a box section that guides the reader through the derivation of the details and includes space for calculation, and homework problems.

At a few spots in the book, the discussion has been oversimplified. For example, the introduction of the “absolute gradient,” more commonly known as the covariant derivative, and the central role it plays in the mathematical realization of the equivalence principle is not rigorous. A student or scientist wishing to acquire a more thorough understanding of the theoretical or mathematical aspects of general relativity should read a more advanced book, like Sean Carroll’s *Spacetime and Geometry: An Introduction to General Relativity* (Addison-Wesley, 2003), Norbert Straumann’s *General Relativity* (2nd edition, Springer, 2013), or Robert Wald’s *General Relativity* (University of Chicago Press, 1984).

In any case, I think anyone interested in learning about this fascinating theory will find *A General Relativity Workbook* to be captivating. The book’s lively style and novel design make it as easy as possible for students and nonexperts to grasp the physical concepts behind the theory. And Moore’s decision to discuss the physical properties of the Schwarzschild metric before introducing the more complicated mathematics required for deriving it from Einstein’s field equations paid off. Furthermore, the book contains a wealth of useful exercises and homework problems, including ones about such exciting and modern topics as cosmic rays, gravitational lensing, inflation, and gravitational radiation from binary pulsars.

I strongly recommend *A General Relativity Workbook* to instructors teaching general relativity and to their students.

**Olivier Sarbach** is a professor at the institute of physics and mathematics at the University of Michoacán in Morelia, Mexico. His research is in classical general relativity.