**Review of “The Springer Handbook of Spacetime” edited by Abhay Ashtekar and Vesselin Petkov**

The word “Handbook” in the title is something of a misnomer: it is perhaps better to think of this book as a collection of mini review articles on various topics in relativity. The best way to use the book is to think of a topic in relativity about which you would say “I wish I knew and understood more about *X*, but I don’t have the time to read a review article about *X*, nor the expertise to understand a typical review article on the subject.” Then look in the book to see if there is a chapter on *X*, and if so, read it. (Then repeat the process for each *X*). Each mini review article comprises a chapter and the chapters are organized in sections that reflect a particular aspect of relativity.

The first two sections, *Introduction to Spacetime Structure* and *Foundational Issues* concentrate mostly on the basic properties of spacetime and on philosophical issues connected with special and general relativity. I found these sections somewhat slow going, not because of a lack of interest in the subject, but rather I suspect because after a certain number of years doing general relativity one develops one’s own attitude towards the foundations of the subject and is therefore less likely to say “I wish I knew more about …”. The next section, *Spacetime Structure and Mathematics*, I found much more enjoyable, particularly because highly technical subjects (such as the initial value formulation, the positive energy theorem, and AdS/CFT) were presented in sufficiently non-technical language that I could understand them.

The next section, *Confronting Relativity Theories with Observations*, consisted mostly of discussions of experiments that can be used to rule out various alternative theories of gravity, though there was also a chapter on quasi-local horizons, and a very nice treatment of the use of relativity in the GPS system. The following section, *General Relativity and the Universe* treated cosmology, including standard topics like the Friedmann-Lemaitre-Roberston-Walker metric, the cosmic microwave background, and inflation, as well as more exotic topics like the use of viscosity in cosmology. The chapters in this section were good; but for the most part, these subjects are already well presented in standard textbooks on general relativity and on cosmology.

The final section, *Spacetime Beyond Einstein*, is on quantum gravity. This section features both general presentations of the problem of coming up with a theory of quantum gravity and particular approaches to this problem: mostly loop quantum gravity but also some other approaches. Since most work on each of the approaches to quantum gravity is usually written for insiders of that approach, it was nice to see in this book articles on these subjects that were somewhat more accessible.

For a comprehensive treatment of general relativity, the book has some odd features: a whole section on philosophical issues in relativity that somehow has nothing by David Malament, John Norton, or John Earman; an entire section on cosmology, but relatively little on black hole astrophysics; hardly any numerical relativity; a section on quantum gravity where the only chapter on string theory is on string cosmology. Nonetheless, I am confident, dear readers of this review, that each of you will find something of value and interest to you in this book. Just do not emulate your obedient reviewer in reading the book cover to cover.

**The Springer Handbook of Spacetime**

Editors: Abhay Ashtekar and Vesselin Petkov (Eds.)

Springer

950 pages | Hardback

9783642419911

Also available as: eBook and Online Enhanced Book

**Price: £166.00**

This work is licensed under a Creative Commons Attribution 3.0 Unported License.

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