Schutz: Next Steps in General Relativity

[h0dgey84bc]

Hi,

I have just read (well read most of :) ) Schutz First Course in Gen Rel, what would be a good book to go on from after this? I thought Schutz was pretty good on the intro to tensors and diff geo, since it approached the subject from the index free way, which I found more satisfying than the approach in D'Inverno that I initially started with, then abandoned.

Thanks

 

[Fredrik]

Wald is definitely the book to read. It may not be the best introductory text, but you have already read one of those. I recommend that you also buy or borrow a book that explains differential geometry using the index free notation. It really helps to learn to work with both. Wald uses the abstract index notation (which makes every tensor equation look like it's describing a relationship between the components of the tensors in a coordinate system, even though no coordinate system is involved). The abstract index notation is superior to the index free notation when it comes to constructing new tensors from existing ones, but it's just confusing in definitions of new concepts (in my opinion).

I really liked Schutz by the way, not for the stuff about general relativity, but for the stuff about special relativity and tensors.

 

[h0dgey84bc]

I think Wald is what I'm ultimatley aspring too, seems a little scary right now though, it's like the Jackson of GR or something, hehe. Surprisingly cheap though, strangely.

I recommend that you also buy or borrow a book that explains differential geometry using the index free notation

I feel like a formal book dedicated to just differential geometry would be a lot of use to me now, I have Schutz's other math methods book, but I've not started on it at all yet...maybe that will be sufficient. I really feel like I need a formal course in differential geometry though, like one would perhaps find on an undergrad maths degree, any books that would provide this?

 

[George Jones]

I think Wald is what I'm ultimatley aspring too, seems a little scary right now though, it's like the Jackson of GR or something, hehe. Surprisingly cheap though, strangely.

An Introduction to General Relativity: Spacetime and Geometry (the real version, not the web version) by Sean Carroll is a little less scary than Wald. Wald has a very good summary of global methods, including singularity theorems, but is not very up-to-date with respect to cosmology.

I feel like a formal book dedicated to just differential geometry would be a lot of use to me now, I have Schutz's other math methods book, but I've not started on it at all yet...maybe that will be sufficient. I really feel like I need a formal course in differential geometry though, like one would perhaps find on an undergrad maths degree, any books that would provide this?

Maybe Schutz's mathematical methods is not scary enough . I recommend The Geometry of Physics: An Introduction by Theodore Frankel or A Course in Modern Mathematical Physics by Peter Szekeres. Szekeres might not cover as much differential geometry as you want, but it covers material more carefully than Schutz, and it covers other stuff, like measure theory, distributions, and Hilbert spaces.

 

[JasonJo]

Hey I'm a math student and I've worked out of Carroll and then Wald. I would like to echo what George Jones said, Carroll into Wald has worked out very well for me. In all honesty, Wald is a step up, but it's not like Griffith's EM to Jackson in my opinion.

If you have the money, try getting both Carroll and Wald. In the beginning those two should suffice to get the "basics" of GR. However later on Wald sometimes gives sketches of arguments and sketches of proofs and refers to Hawking Ellis a lot (especially in the chapter on Singularity Theorems, he does this 3 or 4 times).

 

[Oberst Villa]

Wald's resource letter "Teaching General Relativity" contains some book recommendations (in the 6th paragraph) for General Relativity and Differential Geometry that might be of interest:

http://arxiv.org/abs/gr-qc/0511073