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1、LectureNotesonGeneralRelativitySeanM.CarrollInstituteforTheoreticalPhysicsUniversityofCaliforniaSantaBarbara,CA93106carroll@itp.ucsb.eduDecember1997AbstractThesenotesrepresentapproximatelyonesemester'sworthoflecturesonintro-ductorygeneralrelativityfor
2、beginninggraduatestudentsinphysics.Topicsincludemanifolds,Riemanniangeometry,Einstein'sequations,andthreeapplications:grav-itationalradiation,blackholes,andcosmology.Individualchapters,andpotentiallyupdatedversions,canbefoundathttp://itp.ucsb.edu/~car
3、roll/notes/.arXiv:gr-qc/9712019v13Dec1997NSF-ITP/97-147gr-qc/9712019iTableofContents0.Introductiontableofcontents
4、preface
5、bibliography1.SpecialRelativityandFlatSpacetimethespacetimeinterval
6、themetric
7、Lorentztransformations
8、spacetimediagrams
9、vectors
10、th
11、etangentspace
12、dualvectors
13、tensors
14、tensorproducts
15、theLevi-Civitatensor
16、indexmanipulation
17、electromagnetism
18、di erentialforms
19、Hodgeduality
20、worldlines
21、propertime
22、energy-momentumvector
23、energy-momentumtensor
24、perfect
uids
25、energy-momentumconservation2.Manifold
26、sexamples
27、non-examples
28、maps
29、continuity
30、thechainrule
31、opensets
32、chartsandatlases
33、manifolds
34、examplesofcharts
35、di erentiation
36、vectorsasderivatives
37、coordinatebases
38、thetensortransformationlaw
39、partialderivativesarenottensors
40、themetricagain
41、canonicalformoftheme
42、tric
43、Riemannnormalcoordinates
44、tensordensities
45、volumeformsandintegration3.Curvaturecovariantderivativesandconnections
46、connectioncoecients
47、transformationproperties
48、theChristo elconnection
49、structuresonmanifolds
50、paralleltrans-port
51、theparallelpropagator
52、g
53、eodesics
54、aneparameters
55、theexponentialmap
56、theRiemanncurvaturetensor
57、symmetriesoftheRiemanntensor
58、theBianchiidentity
59、RicciandEinsteintensors
60、Weyltensor
61、simpleexamples
62、geodesicdeviation
63、tetradsandnon-coordinatebases
64、thespinconnection
65、Maurer-Cartanstruct
66、ureequations
67、 berbundlesandgaugetransformations4.GravitationthePrincipleofEquivalence
68、gravitationalredshift
69、gravitationasspacetimecur-vature
70、theNewtonianlimit
71、physicsincurvedspacetime
72、Einstein'sequations
73、theHilbertaction
74、theenergy-momentumtens
