为数学家写的广义相对论

　　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.此书为英文版！

暂缺《为数学家写的广义相对论》作者简介

Guidelinesforthereader
Chapter0
Preliminaries
0.0Reviewandnotation
0.1Physicsbackground
0.2Previewofrelativity
Chapter1
Spacetimes
1.0Reviewandnotation
1.1Causalcharacter
1.2Timeorientability
1.3Spacetimes
1.4Examplesofspacetimes
Chapter2
Observers
2.0Mathematicalpreliminaries
2.1Observersandinstantaneousobservers
2.2Gyroscopeaxes
2.3Referenceframes
Chapter3
Electromagnetismandmatter
PARTONE:BASICCONCEPTS
3.0Reviewandnotation
3.1Particles
3.2Particleflows
3.3Stress-energytensors
3.4Electromagnetism
3.5Matterandrelativisticmodels
PARTTWO:INTERACTIONS
3.6Somemathematicalmethods
3.7Maxwell'sequations
3.8Particledynamics
3.9Matterequations:anexample
3.10Energy-momentum'conservation'
3.11Twoinitialvaluetheorems
3.12Appropriatematterequations
PARTTHREE:OTHERMATTERMODELS
3.13Examples
3.14Normalstress-energytensors
3.15Perfectfluids
Chapter4
TheEinsteinfieldequation
4.0Reviewandnotation
4.1TheEinsteinfieldequation
4.2Ricciflatspacetimes
4.3Gravitationalattractionandthephenomenonofcollapse
Chapter5
Photons
5.0Mathematicalpreliminaries
5.1Photons
5.2Lightsignals
5.3Synchronizablereferenceframes
5.4Frequencyratio
5.5Photondistributionfunctions
5.6Integrationonlightcones
5.7Aphotongas
Chapter6
Cosmology
6.0Review,notationandmathematicalpreliminaries
6.1Data
6.2Cosmologicalmodels
6.3TheEinstein-deSittermodel
6.4Simplecosmologicalmodels
6.5Theearlyuniverse
6.6Othermodels
6.7Appendix:LuminositydistanceintheEinstein-deSittermodel
Chapter7
Furtherapplications
7.0Reviewandnotation
7.1Preview
7.2Stationaryspacetimes
7.3ThegeometryofSchwarzschildspacetimes
7.4Thesolarsystem
7.5Blackholes
7.6Gravitationalplanewaves
Chapter8
Optionalexercises:relativity
8.1Lorentzianalgebra
8.2Differentialtopologyandgeometry
8.3Chronologyandcausality
8.4Isometriesandcharacterizationsofgravitationalfields
8.5TheEinsteinfieldequation
8.6Gases
Chapter9
Optionalexercises:Newtoniananalogues
9.0Reviewandnotation
9.1Maxwell'sequations
9.2Particles
9.3Gravity
Glossaryofsymbols
Bibliography
Indexofbasicnotations
Index