Gravity: Newtonian, Post-Newtonian, Relativistic, Eric Poisson and Clifford M. Will, Cambridge U. Press, 2014. $80.00 (780 pp.). ISBN 978-1-107-03286-6 Buy at Amazon
Gravity: Newtonian, Post-Newtonian, Relativistic is not the usual relativity text. But it’s the one you need if you actually want to calculate something astrophysical without a supercomputer. I know of no other text that compares with this compendium of tricks for calculating observables in the large fraction of the universe that is not near an event horizon. Eric Poisson and Clifford Will, two world-renowned leaders in the field, have produced the ideal manual for anyone who wishes to do calculations relevant to current experiments or upcoming gravitational-wave observations.
In every area of physics, a few problems can be solved exactly, but most others are approximated. In general relativity the exact solutions are fewer than usual, and almost every point of contact between theory and experiment involves some sort of approximation. At the heart of Gravity are those approximations and how they connect Newtonian to general-relativistic gravity. In practice, making the connections is a task notorious for its conceptual issues and involved calculations. The authors’ exceptionally clear writing and deep understanding of the material, however, render their explication accessible at the graduate-student level. (As a graduate student, I relied heavily on the authors’ publications that led to this textbook.)
The first three chapters of the book treat Newtonian gravity. The authors go beyond the standard point-particle orbits and collect classic methods to compute orbits perturbed by spins, tides, and other phenomena associated with extended structures. They also consider perturbations, such as Newtonian perihelion precession and the Kozai mechanism, that arise from additional point particles. Beyond considering orbital dynamics, they also solve classic problems in stellar structure and perturbations. Previous treatments of those topics are scattered throughout the literature, across subfields from astronomy to geophysics to theoretical physics, and over several centuries of notation and terminology changes. The clear, unified presentation in Gravity is a must-read for anyone wishing to absorb the material efficiently.
Chapters 4 and 5 are a whirlwind tour of special and general relativity, intended as a refresher rather than as an introduction. Still, the authors manage to work in lucid treatments of the classic applications of Schwarzschild spacetime, particle orbits, and relativistic stellar structure. The next five chapters form the core of the book. They lay out the fundamentals of the post-Minkowski (weak-field) and post-Newtonian (slow-motion) approximations crucial to almost all calculations tied to experiments. Most importantly, those chapters show how to solve problems relevant to, among other things, GPS timing, the deflection and lensing of light, the precession of binary pulsars, and Gravity Probe B, the satellite mission to measure spacetime curvature near Earth.
The last three chapters—11, 12, and 13—cover in depth three modern applications of the post-Minkowski and post-Newtonian formalisms. Chapter 11 discusses gravitational waves, a topic of great current interest because Advanced LIGO (Laser Interferometer Gravitational-Wave Observatory) and its sister projects are preparing to collect data. The authors show how to go beyond the quadrupole formula to compute gravitational waveforms to the extremely high accuracy needed for upcoming searches; to do so, one needs to include such terms as the nonlinear tails in the post-Newtonian approximation. That is an enormous undertaking—much like the high-order computation of the fine structure constant in quantum electrodynamics—but one that is crucial to guiding the data analysis.
Chapter 12 covers an offshoot of gravitational-wave research—the radiation-reaction problem. Historically, physicists needed to understand the radiation reaction to shore up the initially shaky foundations of gravitational-wave theory. Things went downhill for decades after Albert Einstein’s first paper on waves got the energy flux wrong by a factor of two; also, Einstein relied on an unexamined energy balance argument. In the future, accounting for the radiation-reaction force will be crucial for computing gravitational waveforms and conducting searches for them in the data of any descendant of LISA (Laser Interferometer Space Antenna), a proposed spaceborne gravitational-wave detector.
Chapter 13 closes the book with a self-contained summary of alternative theories of gravity. It updates Will’s classic text, Theory and Experiment in Gravitational Physics (Cambridge University Press, 1981), by covering the current constraints and those soon to come with gravitational waves.
Various accessories enhance the main text. For example, the homework problems, which range from easy to worthy of a journal article, often feature the computation of a number relevant to a current experiment or observation. Nondistracting figures and tables illustrate key points. And text boxes form interesting asides, providing some history or extra calculation without overwhelming the main text.
Poisson and Will’s Gravity is a great textbook for a special-topics graduate course after the introductory relativity course, a crucial study aid for anyone learning about astrophysical relativity and gravitational waves, and a lifelong reference for career researchers.
Ben Owen is a professor of physics at Texas Tech University in Lubbock. In his breaks from analyzing LIGO data, he moonlights as a theorist of astrophysical sources of gravitational waves.
