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1、LectureNotesonGeneralRelativitySeanM.CarrollInstituteforTheoreticalPhysicsUniversityofCaliforniaSantaBarbara,CA93106carroll@itp.ucsb.eduDecember1997AbstractThesenotesrepresentapproximatelyonesemester'sworthoflecturesonintro-ductorygeneralrelativityforbeginninggraduatestudentsinphysics.Topicsincludem
2、anifolds,Riemanniangeometry,Einstein'sequations,andthreeapplications:grav-itationalradiation,blackholes,andcosmology.Individualchapters,andpotentiallyupdatedversions,canbefoundathttp://itp.ucsb.edu/~carroll/notes/.arXiv:gr-qc/9712019v13Dec1997NSF-ITP/97-147gr-qc/9712019iTableofContents0.Introduction
3、tableofcontents
4、preface
5、bibliography1.SpecialRelativityandFlatSpacetimethespacetimeinterval
6、themetric
7、Lorentztransformations
8、spacetimediagrams
9、vectors
10、thetangentspace
11、dualvectors
12、tensors
13、tensorproducts
14、theLevi-Civitatensor
15、indexmanipulation
16、electromagnetism
17、di erentialforms
18、Hodgeduality
19、worldlines
20、p
21、ropertime
22、energy-momentumvector
23、energy-momentumtensor
24、perfect
uids
25、energy-momentumconservation2.Manifoldsexamples
26、non-examples
27、maps
28、continuity
29、thechainrule
30、opensets
31、chartsandatlases
32、manifolds
33、examplesofcharts
34、di erentiation
35、vectorsasderivatives
36、coordinatebases
37、thetensortransformationlaw
38、partialderiv
39、ativesarenottensors
40、themetricagain
41、canonicalformofthemetric
42、Riemannnormalcoordinates
43、tensordensities
44、volumeformsandintegration3.Curvaturecovariantderivativesandconnections
45、connectioncoecients
46、transformationproperties
47、theChristo elconnection
48、structuresonmanifolds
49、paralleltrans-port
50、theparallelpropag
51、ator
52、geodesics
53、aneparameters
54、theexponentialmap
55、theRiemanncurvaturetensor
56、symmetriesoftheRiemanntensor
57、theBianchiidentity
58、RicciandEinsteintensors
59、Weyltensor
60、simpleexamples
61、geodesicdeviation
62、tetradsandnon-coordinatebases
63、thespinconnection
64、Maurer-Cartanstructureequations
65、 berbundlesandgaugetransformat
66、ions4.GravitationthePrincipleofEquivalence
67、gravitationalredshift
68、gravitationasspacetimecur-vature
69、theNewtonianlimit
70、physicsincurvedspacetime
71、Einstein'sequations
72、theHilbertaction
73、theenergy-momentumtens
