General Relativity for Mathematicians

1. Front Matter

   Pages i-xii

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2. Preliminaries

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 1-16

3. Spacetimes

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 17-35

4. Observers

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 36-59

5. Electromagnetism and matter

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 60-110

6. The Einstein field equation

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 111-123

7. Photons

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 124-158

8. Cosmology

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 159-215

9. Further applications

   • Rainer K. Sachs, Hung-Hsi Wu

   Pages 216-249

10. Optional exercises: relativity

    • Rainer K. Sachs, Hung-Hsi Wu

    Pages 250-265

11. Optional exercises: Newtonian analogues

    • Rainer K. Sachs, Hung-Hsi Wu

    Pages 266-272

12. Back Matter

    Pages 273-291

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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).

• Manifold
• Relativity
• Relativitätstheorie
• general relativity
• geometry
• mathematics

• Department of Physics, University of California at Berkeley, Berkeley, USA

  Rainer K. Sachs

• Department of Mathematics, University of California at Berkeley, Berkeley, USA

  Hung-Hsi Wu

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