Welcome to general relativity ("GR")! You skipped here to the end to see where you're going, right? I'm onto you. You want to join the elite, don't you? Good. You've outgrown the "rubber sheet" they put you to sleep with in every pop-physics presentation on Einstein's theory of gravity and you're ready for the real story not only on gravity, but on the very ideas of space and time; maybe even causality itself.
If you really want to understand the math, there is a much bigger hurdle for GR than for special relativity. Most public libraries hav books to take you through the mathematics of SR, but precious few will take you through GR at a comparable level of detail. Our online resources have gotten much better in recent years, but for a long time there was not much out there. Good news, though: this is totally do-able. We're going to eat the whole rhinocerous one bite at a time.
In my search for a foothold on GR, I have collected about a half-dozen books on "tensor analysis," "tensor calculus," "spacetime geometry," etc. There was at least something to be gleaned from most of them, but only one I would recommend for beginners is Dan Fleisch's book, listed under "Other resources" below. It was the Susskind lecture series (see below) that really hit the spot for me, after Fleisch had laid the groundwork. Maybe now I can go back and make more sense of the other books I bought.
If this is really where your interest lies, there's no harm in starting here. If something goes over your head, you can make a note of it and figure out what preparatory material you need to review.
|Content provider||Lecturer||Lecture playlist||Comments|
|various||various||Intro to Tensor Analysis||Start here for an overview.|
|Stanford University||Prof. Leonard Susskind||Lecture Collection | General Relativity (10 lectures)||Dig deeper. This is the gold mine, baby.|
|UC Irvine||Prof. Herbert Hamber||Einstein's General Relativity and Gravitation (20 lectures)||Glutton for punishment?|
A Student's Guide to Vectors and Tensors by Dan Fleisch (the same fellow who starts our "Intro to Tensor Analysis" playlist). Listen to the podcasts and work through the problems on line (with solutions). I highly recommend buying the book. http://www4.wittenberg.edu/sgvt/