Tensors and General Relativity

[pierce15]

Hello all,

I will preface this post with an apology for not putting it in the math/science learning materials section. This would have been the best place to post my question, but for some reason I can't post there.

My question is the following: what depth of understanding must I have of tensors in order to start going through the math behind general relativity? Also, if anyone knows of any particularly good books for learning about tensors, feel free to share them. (I bought this book: https://www.amazon.com/dp/0486658406/?tag=pfamazon01-20, but I'm having a terribly difficult time following it; I strongly agree with the reviewer who wrote that he got lost in the gallimaufry of summations).

Edit: sorry for typos

 

[dEdt]

Most texts on General Relativity (eg Carroll's Spacetime and Geometry) don't assume a knowledge of tensors and instead introduce the topic themselves.

The knowledge of tensors you need to start doing GR is very, very simple. If you know what a linear map is you're halfway there. Carroll on spends a few pages on the subject, and IMO that's all you really need. It's not necessary to buy a whole book on the subject.

 

[pierce15]

Thanks for the reply. I'll look into that textbook

 

[WannabeNewton]

My question is the following: what depth of understanding must I have of tensors in order to start going through the math behind general relativity?

This depends on how rigorous the GR textbook you want to use actually is and how deep into the foundations of GR you want to go-more foundational topics and more rigorous textbooks will make heavier prerequisite demands of the reader.

For an introduction to GR, say at the level of Hartle, Schutz, or Carroll (Carroll is slightly higher level than Schutz) you don't need to worry much (if at all) about the math in the text, you can just jump right in. Hartle is my most favorite introductory GR text with Schutz coming in a very close second. However none of the three aforementioned texts go very deep into the foundations of GR and certainly none of them are mathematically rigorous.

 

[pierce15]

Well, I'm not exactly studying straight-up general relativity. I'm studying cosmology with this book: https://www.amazon.com/dp/0691019339/?tag=pfamazon01-20, which assumes familiarity with (basic, I'm assuming) GR and tensors.

 

[WannabeNewton]

Well if that book by itself doesn't introduce tensor algebra and tensor calculus (i.e. it presupposes knowledge of them) then you can always make use of the numerous GR lecture notes available online that do introduce these tools in the context of GR. Here's a personal favorite of mine: http://www.physics.uoguelph.ca/~poisson/research/agr.pdf (it's not rigorous but it covers all the necessary tools and concepts).

 

[bcrowell]

There is a free online version of Carroll: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html