Gravitational Waves, Volume 1: Theory and Experiments

A superficial introduction to gravitational waves can be found in most textbooks on general relativity, but typically, the treatment hardly does justice to a field that has grown tremendously, both in its theoretical and experimental aspects, in the course of the last twenty years. Other than the technical literature, few other sources have been available to the interested reader; exceptions include edited volumes such as [1] and [2], Weber's little book [3] which happily is still in print, and Peter Saulson's text [4] which appears, unfortunately, to be out of print. In addition to these technical references, the story of gravitational waves was famously told by a sociologist of scientific knowledge [5] (focusing mostly on the experimental aspects) and a historian of science [6] (focusing mostly on the theoretical aspects). The book Gravitational Waves, Volume 1, by Michele Maggiore, is a welcome point of departure. This is, as far as I know, the first comprehensive textbook on gravitational waves. It describes the theoretical foundations of the subject, the known (and anticipated) sources, and the principles of detection by resonant masses and laser interferometers. This book is a major accomplishment, and with the promised volume 2 on astrophysical and cosmological aspects of gravitational waves, the community of all scientists interested in this topic will be well served. Part I of the book is devoted to the theoretical aspects of gravitational waves. In chapter 1 the waves are introduced in usual relativist's fashion, in the context of an approximation to general relativity in which they are treated as a small perturbation of the Minkowski metric of flat spacetime. This is an adequate foundation to study how the waves propagate, and how they interact with freely moving masses making up a detector. The waves are presented in the usual traceless-transverse gauge, but the detection aspects are also worked out in the detector's proper rest frame; this dual discussion is helpful, as it clarifies some of the puzzling aspects of general covariance. Next the treatment becomes more sophisticated: the waves are allowed to propagate in an arbitrary background spacetime, and the energy–momentum carried by the wave is identified by the second-order perturbation of the Einstein tensor. In chapter 2 the waves are given a field-theoretic foundation that is less familiar (but refreshing) to a relativist, but would appeal to a practitioner of effective field theories. In an interesting section of chapter 2, the author gives a mass to the (classical) graviton and explores the physical consequences of this proposal. In chapter 3 the author returns to the standard linearized theory and develops the multipolar expansion of the gravitational-wave field in the context of slowly-moving sources; at leading order he obtains the famous quadrupole formula. His treatment is very detailed, and it includes a complete account of symmetric-tracefree tensors and tensorial spherical harmonics. It is, however, necessarily limited to sources with negligible internal gravity. Unfortunately (and this is a familiar complaint of relativists) the author omits to warn the reader of this important limitation. In fact, the chapter opens with a statement of the virial theorem of Newtonian gravity, which may well mislead the reader to believe that the linearized theory can be applied to a system bound by gravitational forces. This misconception is confirmed when, in chapter 4, the author applies the quadrupole formula to gravitationally-bound systems such as an inspiraling compact binary, a rigidly rotating body, and a mass falling toward a black hole. This said, the presentation of these main sources of gravitational waves is otherwise irreproachable, and a wealth of useful information is presented in a clear and lucid manner. For example, the discussion of inspiraling compact binaries includes a derivation of the orbital evolution of circular and eccentric orbits driven by radiative losses, the frequency spectrum of the radiation, and the dependence of the waveforms on cosmological parameters. In chapter 5 the author tackles a challenging topic: the post-Newtonian theory of gravitational-wave generation, mostly as developed by Luc Blanchet and his collaborators. This topic is extremely demanding, and the author does a good job of describing the main ideas and summarizing the main results. The presentation is detailed, but it is descriptive rather than didactic; this is appropriate, since a systematic development of this topic would surely require an entire book (or two, or three). In chapter 6, which concludes part I of the book, the author discusses the observational confirmation of the existence of gravitational waves that came from a handful of binary pulsars. He provides a detailed derivation of the timing formula that relates each pulse's time-of-arrival to the system's orbital parameters. Measurement of these parameters produce strongly constraining tests of general relativity, and it is the accurate determination of the slowly decreasing orbital period that led to the inescapable conclusion that gravitational waves do, in fact, exist. Part II of the book is devoted to the experimental aspects of gravitational waves: how the detectors work, and how the weak signals are extracted from the noisy data streams. In chapter 7 the author provides a solid introduction to data-analysis techniques, which include the characterization of detector noise by a spectral density function, the matched filtering of signals of known form, and the statistical theory of signal detection and parameter estimation. This last topic is beautifully covered; the author introduces both frequentist and Bayesian views of probabilities, and he (correctly) favours the Bayesian approach to determine the probability distribution function of signal parameters, given the detector's output data. The theory is applied to many types of signals: short bursts, periodic waves, waves from inspiraling binaries, and stochastic backgrounds of cosmological origin. In chapter 8 the author explains the inner workings of (cylindrical and spherical) resonant-mass detectors. The presentation begins with a detailed study of the response a gravitational wave produces in an elastic body. It moves on to the exploration of a simple model for the detector's read-out system, in terms of coupled oscillators. After a survey of noise sources within a resonant bar and a discussion of the standard quantum limit and non-demolition measurements, the author describes the physics of a resonant sphere, whose normal modes of vibrations can reveal each one of the two polarization states of a gravitational wave. Interferometric detectors are the topic of chapter 9, the book's concluding chapter. The author first explains how the passage of a gravitational wave affects the optical path within a simple Michelson interferometer, and he next moves on to the more complicated (and more relevant) case of a Fabry–Perot interferometer. Step by step he adds layers of complexity that eventually produce a more realistic (but still idealized) version of an interferometric detector. And after another survey of noise sources, the author describes the current status of the LIGO and VIRGO detectors. I must say that I especially appreciated the last two chapters on detector modeling. What I like most is the fact that while an understanding of gravitational waves and their sources relies mostly on general relativity and astrophysics, an understanding of detectors relies on a lot more of interesting physics. For example, elasticity theory, thermal physics, and quantum mechanics are required to describe the operations of a resonant bar, while wave and quantum optics are required to model an interferometer; the joining of gravitational-wave physics with these subjects gives rise to a very rich field of study. Chapter 9, however, contains a disappointment: except for a short paragraph at its very end, there is no coverage of LISA, the space-based interferometric detector that would be sensitive to low-frequency gravitational waves. The detection principles of LISA are substantially different from those of Earth-based interferometers, and a detailed presentation at the author's high pedagogical standard would have made a welcome addition to this fine book. For its comprehensive coverage of the theoretical and experimental aspects of gravitational waves, and for the high quality of its writing, this book is a truly remarkable achievement. I recommend it with great enthusiasm to anyone interested in this exciting topic. A particularly appealing feature of the book is the suggestions for further reading that can be found at the end of each chapter; this gateway into the technical literature will be most useful to anyone wanting to learn more. References [1] Ciufolini I, Gorini V, Moschella U and Fre P (eds) 2001 Gravitational Waves (Studies in High Energy Physics, Cosmology and Gravitation) (London: Taylor and Francis) [2] Blair D G (ed) 2005 The Detection of Gravitational Waves (Cambridge: Cambridge University Press) [3] Weber J 2004 General Relativity and Gravitational Waves (New York: Dover) [4] Saulson P R 1994 Fundamentals of Interferometric Gravitational Wave Detectors (Singapore: World Scientific) [5] Collins H 2004 Gravity's Shadow: The Search for Gravitational Waves (Chicago, IL: University Of Chicago Press) [6] Kennefick D 2007 Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves (Princeton, NJ: Princeton University Press)