General Relativity for Mathematicians (Graduate Texts in Mathematics, 48) by R.K. Sachs (PDF)

Description

This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva­ tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. 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 !ike cosmology can be learned without so me hard work on boring detaiis 3. 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 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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

⭐as a companion volume.Penrose’s

⭐is also a good companion volume.

⭐It is too bad this book is out of print, as it is nicely written and addresses a mathematically sophisticated reader with a solid background in differential geometry. It is written by two very competent mathematicians, and still could be read as background for more modern developments in general relativity, particularly singularity theorems and as mathematical preparation to the current research in quantization of gravity. It could serve as a textbook in a class the mathematical foundations of general relativity at the graduate level.

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