為數學家寫的廣義相對論

內容概要

While using this book in classes, we found that our canonical reader can learn nonquantum physics rather quickly. Indeed, equipped with geometric intuition and a facility with abstract arguments, he is in a position to deal directly with the general, currently accepted models used in relativity without being handicapped by the prejudices that inevitably come with years of Newtonian training in the standard physics curriculum. However, this shortcut does involve a price: one cannot really see the diversity of special cases behind the deceptively simple foundation without spending more time than a mathematics student normally can or should. We have felt for a long time that a serious effort should be made by physicists to communicate with mathematicians somewhat along the line of this book. We started with the aim of keeping the physics honest, keeping th9 mathematics honest, and keeping the logical distinction between the two straight. But we were ill-prepared for the attendant trauma of such an undertaking.

書籍目錄

Guidelines for the reader Chapter 0 Preliminaries   0.0 Review and notation   0.1 Physics background   0.2 Preview of relativity Chapter 1 Spacetimes   1.0 Review and notation   1.1 Causal character   1.2 Time orientability   1.3 Spacetimes   1.4 Examples of spacetimes Chapter 2 Observers   2.0 Mathematical preliminaries   2.1 Observers and instantaneous observers   2.2 Gyroscope axes   2.3 Reference frames Chapter 3 Electromagnetisim and matterChapter 4 The Einstein field equationChapter 5 photonsChapter 6 CosmologyChapter 7 Further applicationsChapter 8 Optional exercises:relativityChapter 9 Optional exercises:Newtonian analoguesGlossary or symbolsBibliographyIndex of basic notationsIndex

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