Please can someone recommend some books on 'higher-level' (couldn't think of a better way to phrase...) books on GR? I've read over half of Wald (General Relativity) and I'm about to finish Carroll (Spacetime and Geometry). I didn't really enjoy reading Wald (sacrilege!), but I've really really enjoyed Spacetime and Geometry - I felt it was more modern, and almost like I was being lectured in the subject. For some reason, it didn't feel the same with Wald, most probably because I read Wald from a .pdf and Carroll from hardback.
I really enjoyed the Black Hole aspects of S&G, but I feel that I'm little weak on gravitational waves. I'd also like to see some more advanced differential geometry too, like spinors and tetrads (even though I don't know what they are yet, they sound important). If someone could recommend a book with the feel of Carroll but more advanced content, I'd be extremely grateful.
I feel the answer to my question is to go back and try Wald again, however I would like some other opinions!
I came up with the some suggestions to begin to even start looking at GR and SR in a way that a mathematician would.
Make a disciplined effort to get through Ted Shifrin's texbook (.pdf free to everyone) on differential geometry. This will give a good review of some much needed analytical geometry and introduce the notion of covariant differentiation, parallel translation, and geodesics - which are pinacle ideas used in GR and SR.
If the ideas in this book sit well and you are feeling comfortable getting through (most of) the exercises, then take a look into purchasing Tensors: The Mathematics of Relativity Theory and Continuum Mechanics, by Anadijiaban Das. This book is a relatively expensive, but worth every penny; especially if you're serious about learning the anatomy of GR and SR. It is a mathematicians approach to introducing the machinery needed to study problems in GR and SR - not to mentioning its rewarding rigor.
if you are looking for some broad lectures that give a good overview of the mathematics needed to start being a better physicist, take a look at Fredric Schuller's lectures on the geometrical anatomy of theoretical physics.. He is by far one of the most precise lecturers I have ever learned from. These lectures encompass a vast amount of topics that are pertinent in studying physics - especially Einstein gravity. Getting through these lectures from start to finish will definitely help understand my comment: spacetime is a four-dimensional topological manifold with a smooth atlas carrying a torsion-free connection compatible with a Lorentzian metric and a time orientation satisfying the Einstein equations.