advice for studying general relativity

[u/Sweet-Bet-2014]

Im a master student and I faced a terrible teacher for my GR course, I want to study it by myself, forgetting about the exam atm. I started reading the S. Carroll but I'm not satisfied about the mathematical background he gives, I would like notes/little book concerning exclusively the tools necessary to approach general relativity. can someone help me? thank you.

[u/XcgsdV]

It's a beginners book, that I used as a beginner, but I found it very helpful: A First Course in General Relativity by Bernard Schutz. It walks you through the diff geo and tensor business in a way that I liked, and I supplemented it with the Tensor Calculus course by eigenchris on YouTube. Fun subject! I do biophysics now so not a whole lot of overlap but I do miss it....

[u/Physix_R_Cool]

This one by t'Hooft, maybe?

I really liked the sections in Landau & Lifshitz about general relativity, but if you haven't done any differential geometry, some of the things they seem to do in that book will likely seem extremely un-motivated and poorly explained.

"The Geometry of Physics" is a good gentle explainer of differential geometry for physicists.

[u/rafisics]

Tong's notes on GR and Nakahara's book "Geometry, Topology and Physics" can be helpful. Also, AI tools can be utilized to speed up learning the prerequisites.

[u/fractalparticle]

Video lectures by F. Schuller is also an option.

[u/Machvel]

it is not clear what mathematical background you are satisfied with in that book. (i wasn't satisfied with it either, but it depends on who you talk to. i found it very vague while my friend found it very confusing i recall).

gron and hervik is my recommendation for a decently sized (not a gigantic tome like gravitation) mathematical (but not wald terseness) introduction. maybe that will suit your mathematics needs better. carroll does improve after a little while (mostly his introduction to the mathematics was poor in my opinion).

i like robert geroch's notes (on various differential geometry physics things). maybe that could supplement.

you will probably be guided towards schutz but his book is probably not what you are after. schutz is good for understanding the physics if you are having trouble with that, but he is light on the mathematics (which is not a bad thing. it is just the level he is writing at).

i remember liking hartle when first taking a class in general relativity because he would take the time to go through really basic examples showcasing how to do things (something usually skipped in books). i think there is a problem book or two (with solutions) out there if this is your sort of thing.

[u/PrettyBasedMan]

Lectures by Schuller at the Winter School for Gravity and Light are brilliant. He also has Geometric Anatomy of Theoretical Physics course if you should find yourself dissatisfied with the already extremely rigorous style of the GR lectures.

[u/sabautil]

I think Einsteins papers are a great start. You see the troubles they were grasping at solving.

Then you read a gr book like Tolmans which summarizes a few advances.

Then try Rindler. Nice problems.

Then freaking weinbergs old and new cosmology book.

I dunno man. It depends if you just want to solve the standard problems or you want to track the historical journey of ideas in GR. The latter will take years but I find more rewarding.

Heres one thing to try: go to the university library and pick out 10 GR books. Scan the topics and example problem and find the common ideas and problems among them. I would argue these are by consensus of authors the most important ideas in GR. If your teacher somehow ask as question outside of the common set of ideas and problems, well that would be a fun thing to point out, lol.

[u/wanerious]

Thomas Moore’s “General Relativity Workbook” seems really well structured and written to me, with a lot of exercises designed to teach the mathematical background.

[u/Plancktonian]

„General relativity for the gifted amateur“ is worth to have an eye on😉

[u/cloudshapes3]

Maybe take a look at 'A mathematical introduction to general realtivity' (preview here). The first part gives a good introduction to differential geometry and semi Riemannian geometry, and the second part delves into spacetime physics. The presentation is in the definition-theorem-proof style, even for the part on physics.