Can someone suggest a textbook that treats general relativity
from a rigorous mathematical perspective? Ideally, such a book
would - Prove all theorems used - Use modern "mathematical
notation" as opposed to "physics notation", especially with
respect to linear algebra and differential geometry - Have
examples that illustrate both computational and theoretical
aspects - Have a range of exercises with varying degrees of
difficulty, with answers An ideal text would read a lot more
like a math book than a physics book and would demand few
prerequisites in physics. Bottom line is that I would like a
book that provides an axiomatic development of general
relativity clearly and with mathematical precision works out the
details of the theory. Addendum (1): I did not intend to start a
war over notation. As I said in one of the comments below, I
think indicial notation together with the summation convention
is very useful. The coordinate-free approach has its uses as
well and I see no reason why the two can't peaceful