General Relativity for Mathematicians - ISBN:038790218X

General Relativity for Mathematicians

Date: 15 April 2011, 02:22

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Reviews:
--I took the course on which this book is based from Mr. Sachs at UC Berkeley when the book was in the form of printed handouts.
This book is aimed at readers with a fairly advanced level of mathematical background - differentiable manifolds and some basic riemannian geometry (e.g Warner "Differential Manifolds"). This background is assumed and a prospective reader without this knowledge would be well advised to use the Hawking and Ellis book The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics) as a companion volume.
Penrose's Techniques of Differential Topology in Relativity (CBMS-NSF Regional Conference Series in Applied Mathematics) (CBMS-NSF Regional Conference Series in Applied Mathematics) is also a good companion volume.
--As a student of physics, I'm always plagued by the presentation of any modern physics. Questions of "where does this come from" or "what does this mean" are never answered and rather students are expected to simply work calculations until those questions fade away, answered (or rather unanswered) by a new familiarity with just how to do calculations. It is as if understanding the theory was only a means to an end.
Anyway, this book went a long way for presenting the material in a way that satisfies those questions. Even if the answer is just "it seems somewhat plausible to define something that way based on what we observe experimentally", the book actually gets down to it and says that and defines it -- rather than just assuming that you knew it was obvious to describe particles using a mass density function, for example.
Also, the book actually covers not just GR, but also electrodynamics (the foundational way) and also matter models. It's worth it just for the chapter on matter.

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