# New Book: Special Relativity in General Frames by Gourgoulhon

1. Dec 31, 2013

### George Jones

Staff Emeritus
https://www.amazon.com/Special-Relativity-General-Frames-Astrophysics/dp/3642372759/ref=pd_sim_b_6

http://www.springer.com/physics/the...+computational+physics/book/978-3-642-37275-9

I have just ordered (actually, my wife did, but she has yet to realize this ) this new, comprehensive, advanced book on special relativity. From the content (check the above links for more details), this seems to be an amazing book. Some of the material can be transferred wholesale to frames in general relativity.

1 Minkowski Spacetime
2 Worldlines and Proper Time
3 Observers
4 Kinematics 1
5 Kinematics 2
6 Lorentz Group
7 Lorentz Group as a Lie Group
8 Inertial Observers and Poincare Group
9 Energy and Momentum
10 Angular Momentum
11 Principle of Least Action
12 Accelerated Observers
13 Rotating Observers
14 Tensors and Alternate Forms
15 Fields on Spacetime
16 Integration in Spacetime
17 Electromagnetic Field
18 Maxwell Equations
19 Energy–Momentum Tensor
20 Energy–Momentum of the Electromagnetic Field
21 Relativistic Hydrodynamics

Last edited by a moderator: May 6, 2017
2. Dec 31, 2013

### WannabeNewton

My university lets me download Springer ebooks for free so as soon as I saw this post I downloaded the pdf and my god does this look incredibly, incredibly awesome. This book reminds me a lot of Sachs and Wu's "General Relativity for Mathematicians" but set in more modern notation that's physicist friendly. Chapter 3 in particular looks quite amazing. I'll be ordering the physical text as soon as physically possible. Thanks for bringing this text to attention George :)

Although I must say, with the excitement this book has brought upon me (just by looking at the contents and skimming through chapters 3 and 18, I haven't even delved into the book in detail!) you have made it 100x harder for me to focus all my attention on QFT because there's a very big chance that this book will end up consuming all my time in the coming spring semester :tongue2:

EDIT: And the author uses $\nabla_{\mu}$ instead of the incredibly annoying $;$ for covariant derivatives...this book can't get any better

Last edited: Dec 31, 2013
3. Jan 14, 2014

### bolbteppa

Yeah the contents of that book stunned me when I first looked, also looks like an advanced book that will throw in baby examples to re-enforce the material - something I'm unfortunately a big fan of. If you do go through parts of it & find cool things I'd love to get motivation to read this book from it ;)

4. Jan 23, 2014

### WannabeNewton

After reading various chapters of the book in much more detail, I can undoubtedly say that the book is absolutely brilliant and easily the best SR book I've personally ever read. In fact the way it presents the chronogeometric framework of SR as well as the mathematical apparatus of tensor fields and tensor calculus on space-time makes it better than a lot of standard GR books IMO (with regards to foundations that is).

My favorite topic in SR and GR has always been rotation so I gravitated towards chapter 13 the most, which deals mostly with the relativistically rotating disk. It goes into great depth on the local and global clock synchronization on the disk, the Sagnac effect, slow clock transport, and the Ehrenfest paradox so as far as rotation in SR goes this chapter is basically perfection. Also there is an entire chapter devoted to the formalism of angular momentum in SR. The book is worth buying just for this.

As the title suggests, the book has a very systematic treatment of frames in SR (which the author carefully distinguishes from coordinate systems); in particular, it spends quite a bit of time developing the 4-rotation of a frame in terms of the Fermi-derivative, which it then later relates to rotation relative to gyroscope axes. Of course standard GR texts like MTW also do this but I felt that this book went into more detail on the topic and in a much clearer manner than MTW. It is also goes into much needed detail on the difference between simultaneity surfaces (as determined by the Einstein simultaneity convention) and orthogonal hyperplanes relativized to an arbitrary observer. MTW does this as well but I feel like this book has a much clearer exposition of this mainly because it writes out explicitly the calculations of the simultaneity hypersurfaces for rotating as well as linearly accelerating observers.

Most of the contents of chapters 17-20 aren't as mind-blowingly amazing as those of chapters 2,3,10,12,13 as I had already seen them done in more detail using more covariant language in Wald's text, Geroch's notes and the likes but there are certain parts of said chapters that stand out like the detailed discussion of synchrotron radiation. Unfortunately, I haven't gotten around to reading chapter 21 yet.

Also there is no shortage of surprisingly helpful and detailed diagrams throughout the book; it seems like they show up every other page.

Honestly my only complaint is regarding the awkward idiomatic phrases that show up very frequently throughout the book. I suppose it's a side effect of the fact that the English version of this book comes from a French translation but it's no big deal. Also chapters 7 and 8 feel out of place with respect to the rest of the book but that may just be a result of my lack of interest in the subject matter of chapters 7 and 8.

To reiterate, this book is superior to every SR book I have ever seen