This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who:
- are mathematics graduate students with some knowledge of global differential geometry
- have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting
- appreciate mathematical clarity, but are willing to accept physical motivations for the mathematics in place of mathematical ones
- are willing to spend time and effort mastering certain technical details, such as those in
Section 1.1
Each book disappoints some readers. This one will disappoint:
- physicists who want to use this book as a first course on differential geometry
- mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back- ground, the essentials of a subject like cosmology can be learned without some hard work on boring details
- those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful
- those who want an encyclopedic treatment (the books by Hawking-Ellis, Penrose, Weinberg, and Misner-Thorne-Wheeler go further into the subject than we do; see also the survey article, Sachs-Wu).
- mathematicians who want to learn quantum physics or unified field theory (unfortunately, quantum physics texts all seem either to be for physicists, or merely concerned with formal mathematics).