I read this book for the first time quite some ago, and recently re-read it.
(Full disclosure: I haven’t been paid in anyway to write this, I just really like this book.)
Learning real general relativity on your own is a tough task. For the most part, most of the literature out there is either dense academic papers or books where the author boiled away all the math (and all the real thinking and understanding) in an attempt to appeal to a mathematically illiterate crowd. The traditional way to bridge this gap between “too dumbed down to have substance” into “advanced reasoning and understanding of the subject” is to take a university course. Sit in a classroom, and ask a real person questions until you understand. Obviously, not all of us are able enroll in the physics program at the nearest university.
“General Relativity Demystified” is the self help book you’re looking for that bridges the gap. It doesn’t treat you like an idiot, it doesn’t regard you as unworthy. It treats you as a student, an intelligent person looking to learn.
Be forewarned though, if you hate math, physics, etc, you’re not gonna like this book. If you don’t have a strong background in calculus, physics and linear algebra, (AP high school classes won’t do the trick) you’ll probably want to build one up. Any engineer, scientist, or mathematician should be able to trudge through the book with no problems.
The actual math behind General Relativity itself is somewhat unique, in that it requires a depth of understanding that exceeds even thorough coursework in mathematics. Luckily, “General Relativity Demystified” takes you from a good understanding of physics and calculus, and builds up the somewhat unique and abstract mathematics of tensors and one forms absolutely essential in the theory. It even holds your hand through the development of complex operations like finding the Riemann .
Once you’ve plowed through this part of the book though, you get into the theory. Shortly after introduction of the Theory, and the crucial equation, , the author takes you into examples that help you get a good handle for doing actual computations in General Relativity, with trivial examples, as well as walking you through some academic papers published recently. Other important examples (eg, calculation of the Schwarzchild radius, etc.) follow explanation of the core theory.
I really enjoyed this book. If you’re looking to really (and I mean really) learn the theory of General Relativity, this is the book you want. I’ve actively looked for self-teaching GR books that can even come close to rivaling this one, and haven’t found it.