Mathematics – Logic
Scientific paper
Feb 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cqgra..28d9002d&link_type=abstract
Classical and Quantum Gravity, Volume 28, Issue 4, pp. 049002 (2011).
Mathematics
Logic
Scientific paper
As is clearly stated in the preface, this book is a fresh rewrite of Narlikar's published lecture notes [1] from 1978, resulting in a unique historical perspective with a modernized presentation. For workers in the field, this book provides a fascinating glimpse of the state of the art 30 years ago, but there are some inevitable idiosyncracies which might make it less useful to the beginner, especially those attempting to read this book on their own.
The author is well-known for his informal, readable style, and this book is no exception. Although the treatment is overly algebraic from this reviewer's modern perspective, that is not necessarily a drawback, and does accurately reflect contemporary usage. This text is a `math first' approach to relativity, presenting the tensor calculus first, and the physics second. Not surprisingly given the author's interests, there is an emphasis on cosmological applications.
After a quick review of special relativity, the book jumps right in with a fairly standard introduction to tensor calculus, followed almost immediately by chapters on Einstein's equations, the Schwarzschild solution, experimental tests, relativistic astrophysics, and black holes, followed in turn by several chapters on cosmology.
This new text is a faithful adaptation of the earlier text, with essentially identical tables of contents. In fact, the only notable differences are the opening chapter summarizing special relativity, a brief new chapter on gravitational radiation, and the exclusion of a lecture on the Steady State Theory — and that material appears separately in the author's cosmology text [2]. Some of the material, such as the excellent chapter on symmetries, is largely identical to the original, but most of the material has been extensively rewritten, with most of the changes being to presentation, rather than content.
There are some seldom seen gems in this book, such as the aforementioned discussion of symmetries, the extensive discussion of cosmology, a formula for Lorentz transformations in an arbitrary direction, and numerous discussions of early work in the field, complete with original references.
My only real quibble with this book (apart from the use of signature (+ - - -) is that, without comment, it makes some rather sophisticated assumptions about the reader. Chapter 1, the self-described `crash course' in special relativity, expects the reader to be comfortable with standard but nontrivial manipulations of Maxwell's equations, with hyperbolic trigonometry, and to be able to comprehend a statement that Newton's first law `remains as it is' in special relativity, without any statement of the law itself. Tensor notation is also introduced much too quickly in this chapter, although this topic is revisited later in more detail. These are not unreasonable assumptions about the intended audience, who are likely to be graduate students in physics or workers in the field. But the addition of a few explanatory remarks, or an explicit statement of the intended audience, might have encouraged the less experienced reader to keep reading.
In summary, this is an excellent book, which researchers in relativity will treasure for its historical perspective. Instructors of a first course in general relativity who are seeking a `math first' approach should definitely take a look, although they should be prepared to explain some missing details in the presentation.
References
[1] Narlikar J V 1979 Lectures on General Relativity and Cosmology (London: Macmillan)
[2] Narlikar J V 2002 An Introduction to Cosmology (Cambridge: Cambridge University Press)
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