Self-Study General Relativity: After Multivariate Calc in HS

[SirMadame]

I just finished multivariate calculus (without any linear algebra experience yet) and I am seeking out a path to understanding General Relativity. I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR, and what corresponding textbooks I should get from those fields. Also, what General Relativity textbook would be best suited for me with my limited mathematical experience. I am still in high school, so I cannot reference any university material directly.

 

[PeterDonis]

what General Relativity textbook would be best suited for me with my limited mathematical experience

You might try Carroll's online lecture notes:

https://arxiv.org/abs/gr-qc/9712019

These notes should be reasonably accessible if you are familiar with multi-variable calculus; they develop the key ideas of differential geometry from that base.

 

[PeterDonis]

I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR

If you are familiar with multi-variable calculus, you probably have enough mathematical background to start learning GR (for example, from the notes I linked to in my previous post).

What you really need is the physical background. You need to be reasonably familiar with Newtonian physics (three laws of motion and gravity) and with classical electrodynamics (Maxwell's Equations and the Lorentz force law). Unfortunately I don't know of good introductory textbooks for these subjects, but many high schools have physics classes, so you might be able to take one, or to ask your school's physics teacher for suggestions.

 

[robphy]

Can you be more specific about the goal to "understand GR"?

https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20

http://www.eftaylor.com/download.html#special_relativity
http://www.eftaylor.com/spacetimephysics/
http://www.eftaylor.com/exploringblackholes/

http://www.gravityfromthegroundup.org/

http://pages.pomona.edu/~tmoore/grw/
http://pages.pomona.edu/~tmoore/grw/Resources/GRWC1.pdf
http://pages.pomona.edu/~tmoore/grw/Resources/GRWBook.pdf [sample]

https://www.youtube.com/user/eigenchris/playlists
looks pretty good, from what I have seenHere is my ancient website (relocated from its original location) that I made in 1995 when I was a grad student (and when the web was young). It was heavily based on Geroch's "General Relativity from A to B"
http://visualrelativity.com/LIGHTCONE/