On the plane trip back from Washington DC I read the book An Introduction To Black Holes, Information And The String Theory Revolution: The Holographic Universe 
by Leonard Susskind and James Lindesay.
This is a pretty cool book, I must say. First of all, however, we should address the word “Introduction” in the title of this book. On page three of this text (the first full page after the preface) the Schwarzchild metric is written down. Now this sounds like less than an introduction, but really it is a red herring. The book is actually easily readable by anyone who has taken an introduction to general relativity and a good course in quantum theory. I’d say an advanced undergrad could easily grok this book. I make this judgement from the fact that I was able to go through the book in one planeflight.
So what about the quality of the book? There are, basically, three parts to this book. I’m betting that it is based on lecture notes from the two authors: there seems to be major differences in the writing styles for the different sections. Part 1 is “Black holes and mechanics” , part 2 is “Entropy bounds and holography”, and part 3 is “Black holes and strings.” Of these, Part 1 is the largest and takes up most of the book. Which is good, because this is the most interested and best part of the book. In part 1, at a level lacking deep rigor, but a level comfortable for many physicists, the authors introduce the basics of black hole geometry, quantum field time in curved spacetimes, entropy calculations in such spacetimes, black hole thermodynamics and the information paradox for black holes. All in slightly less than a hundred pages. Hence the word “introductory”! This is not a book for those who want to become experts in this stuff, but none-the-less, this is a very beatiful introduction to some really cool ideas. My only major issue with this part of the book is the notation and “words” used to describe quantum theory, and in particular density matrices. If there is one thing quantum information scientists can be proud of, it is their clean and clear notation and exposition about quantum information. I guess everytime I see someone talk about information in quantum theory nowdays, it feels strange if they aren’t using the language of quantum information science. Oh, and for some reason they call the no-cloning principle the no-xerox principle.
Parts 2 and 3 of this book are interesting, but are not as tight as the first part. The entropy bounds deserve a lot more time than is devoted here, I think. But still one gets the basic ideas. Part 3 is very strange because it is so small (less than twenty pages.) It explains, in a very very rudimentary manner, the AdS-CFT correspondence (that supergravity in a certain anti-de Sitter universe can be mapped to a conformal field theory on the boundary of that space.) It’s nice to see this exponsition, but too many details were left out for me to really feel that I got any intuition about this important correspondence.
In total, this is a very nice book and I would definitely recommend it to nonexperts who know the general relativity and quantum theory necessary to understand the book. Part 1 is pretty smooth, I must say. There is only one thing which really bothered me about the book, and that was the lack of references. One of the purposes a book like this can serve is to point the reader to the more rigorous papers dealing with this subject. Unfortunately, the book has only ten references. This is a real shame.
Oh, and by the way, Susskind is, of course, famous for his belief in the anthropic principle. Fortunately it doesn’t make it’s appearance in this book (not that I have strong feelings about this subject 😉 )
Oh, and I especially liked the candor in this passage from the conclussion:
The theory of black hole entropy is incomplete. In each case a trick, specific to the particular kind of black object under study, is used to determine the relation between entropy and mass for the specific string-theoretic object that is believed to represent a particular black hole. Then classical general relativity is used to determine the area-mass relation and the Bekenstein-Hawking entropy. In no case do we use string theory directly to compare entropy and area. In this sense the complete universality of the area-entropy is still not fully understood.
