This is a book review of An Introduction to General Relativity and Cosmology, 2nd Edition by Jerzy Plebański & Andrzej Krasiński.
An Introduction to General Relativity and Cosmology, 2nd Edition*, by Jerzy Plebanski and Andrzej Krasinski (Cambridge University Press), 2024. Pp. 577, 17.5 × 24 cm. Price £69.99 (hardbound, 978 1 00 9415620).
Both authors are well known for their highly mathematical approach to General Relativity. Some might quibble with the title; of the many books I've read covering both GR and cosmology, this book is both one of the longest and the most mathematical. The second author (the first died in 2005) is aware of the tension between the title and the contents, mentioning it in the preface to this second edition, and justifies calling it an "introduction" because not all topics are covered and because no prior knowledge of GR or differential geometry is assumed, though knowledge of calculus, Special Relativity, classical mechanics, and electrodynamics is assumed (thus one could start learning GR and cosmology with this book, though the author notes that "[it] takes a careful reader to some height of advancement".) This is very much a "maths first" book which, despite the author's caveat, covers a large range of topics; that it also does so to a significant depth while "showing much of the work" explains the length. So what is the attraction of a book which covers several topics in a fair amount of detail, as opposed to a really introductory book then additional in-depth books for more specific topics? One possibility is that it is a good book if one wants to learn GR in some detail with applications to many fields presented in a uniform notation (different notation schemes, especially regarding signs, are a constant concern when studying GR); apart from worked examples in the main text, there are exercises at the end of most chapters (no solutions, but the last chapter is entitled `Comments to selected exercises and calculation'). Another is that it is very well written, perhaps surprising since neither the second nor (as far as I know) the first author is a native speaker of English. I also enjoyed the footnotes, which are often comments on the history of the topic. Electrically charged black holes (Kerr--Newman if they are spinning, Reissner--Nordström if not) often get short shrift because they are thought to be rare. This book, though, has a fair amount of discussion on them, highlighting many interesting and unexpected (at least for me) aspects. This book has a very different balance among the various topics than that of otherwise broadly similar books. More detailed discussion of those related to our Universe can be found elsewhere, but this book is the place to go for interesting if not necessarily relevant details which are hard to find elsewhere, in addition to those reasons mentioned above.