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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、dierentialforms

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、dierentiation

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、theChristoelconnection

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