GR textbook to prepare for gravitational waves

[madness]

I've been given Gravitational Waves: Theory and Experiments Volume I to read for a project. The problem is, I haven't learned General Relativity to a high enough level and the book is proving very difficult for me. The book dives straight into linearised gravity in the first chapter, and the field-theoretical approach to GR in the second chapter. Can anyone give me some recommended reading to help bring me up to the necessary level to understand this book?

Thanks in advance for any replies.

 

[malawi_glenn]

we have science book sub-forum where there are many discussion about this.

My advice is the book by ta-pei Cheng and the book by hobson (the first 50% of it)

 

[madness]

What I'm really looking for is a book that is likely to be available in my university physics department library and includes linearised gravity and ideally the field theoretical approach too.

 

[malawi_glenn]

Yes but I have no idea what books you have available.. how would I? Why don't you just ask the professor who gave you the project and the Gravity Wave book for advices regarding this? He/she should know which books are available.

It all depends on how much special relativity, tensor notation and differential geometry you know.

Also the book by Maggiore contains a bibliography section, you could check it you for further hints.

I can also give you a couple of good pdf's about General Relativity if you send me a PM with your e-mail.

 

[George Jones]

General Relativity: An Introduction for Physicists by Hobson, Efstathiou, and Lasenby has a couple of good, introductory chapters on linearised gravity and gravitational waves. If your library doesn't have it, you could use interlibrary loan to get it.

Off the top of my head, I don't know of the good introduction to the field-theoretical approach. In fact, judging by its table of contents, Maggiore's chapter 2 looks quite interesting. For this, and other reasons, I think that I'll get Maggiore's book. Thanks! See

http://www.iop.org/EJ/abstract/0264-9381/25/20/209002

for a review of the book.

 

[madness]

Thanks for the replies. I realize that you won't know exactly what's in my library but I thought at least you might know which books are likely to be in a standard university physics library. My current knowledge of relativity is a bit patchy, consisting of parts of courses here and there and a small project on GR. I have learned things like covariant differentiation and parallel transport from Ray d'Inverno's book, but never taken a full course on differential geometry. I will take a look at Maggiore's bibliography and see what I can get from the library.
Thanks for your recommendation George Jones, I'll see if I can get a hold of it. Glad to hear that I've introduced you to a new book! It's proving difficult for me (a final year undergraduate) but I'm sure you will have no problem.

Thanks for helping.

 

[malawi_glenn]

I also recommended the text by Hobson in my first post, it is a modern clear and "math first" book. It first treats SR without tensor notation, then introduces differential geometry and tensors. After that it treats SR and electromagnetism in covariant tensor notation and then moves on the GR and Einsteins equations. After than, some applications are treated and the book ends with cosmolgy and the final chapter is devoted to a Variational derivation of GR (which is where Maggoire's book starts hehe)

So if you study chapter 1-10 and the last chapter you can surley start to study Maggoire's text, also the book of Hobson have two chapters on Gravitaional waves if I remember correctly ;-)

It is a really nice book, I strongly recommend it.

 

[Daverz]

Sean Carroll's online notes may be of help in getting up to speed. Start with his 3 hour primer on video:

http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Carroll/

Ohanian covers linearized gravity before getting into tensor calculus. This allows him to cover gravitational waves before presenting the full Einstein equation. This would be my first recommendation for someone with a strong physics background. Also look for the books by Schutz, d'Inverno, and Carroll.

I'm not quite sure what you mean by "field theoretic". This brings to mind the online book Fields by Siegel, but I think that would be too much generality when you need to get up to speed quickly.

 

[madness]

From what I can gather, the field-theoretic approach treats the perturbation as a field in flat spacetime and uses classical field theory to approach the problem. I haven't learned much of it though so this may be wrong.

 

[Daverz]

From what I can gather, the field-theoretic approach treats the perturbation as a field in flat spacetime and uses classical field theory to approach the problem. I haven't learned much of it though so this may be wrong.

See if you can find Ohanian, Gravitation and Spacetime. There's a 2nd edition.

Table of Contents here:

https://www.amazon.com/dp/0393965015/?tag=pfamazon01-20

He covers linearized gravity and gravitational waves before tackling Riemannian geometry.

Also, it sounds like you have enough preparation for Sean Carroll's graduate text.

 

[madness]

I've had a look at Carroll's primer and I would say that it roughly covers all the stuff I've already learned (although I've learned more tensor calculus and variational things like the Palatini approach and a bit less cosmology). I'll see if I can find the books by Ohanian, Hobson or Carroll in my library.
My problem with the Maggiore book on gravitational waves is that I can barely work out any of the missing steps, eg finding the linearised Riemann tensor. Apart from that I feel like I have an understanding of what he's trying to prove and why he's trying to prove it.
Thanks for the help.

 

[siyphsc]

look into schutz, wald, and Misner Thorne Wheeler.