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1、INTRODUCTIONTOGENERALRELATIVITYG.’tHooftInstituteforTheoreticalPhysicsUtrechtUniversity,Princetonplein5,3584CCUtrecht,theNetherlandsversion8/4/20021PROLOGUEGeneralrelativityisabeautifulschemefordescribingthegravitationalfieldandtheequationsitobeys.Nowadaysthistheoryiso
2、ftenusedasaprototypeforother,moreintricateconstructionstodescribeforcesbetweenelementaryparticlesorotherbranchesoffundamentalphysics.Thisiswhyinanintroductiontogeneralrelativityitisofimportancetoseparateasclearlyaspossiblethevariousingredientsthattogethergiveshapetoth
3、isparadigm.Afterexplainingthephysicalmotivationswefirstintroducecurvedcoordinates,thenaddtothisthenotionofanaffineconnectionfieldandonlyasalaterstepaddtothatthemetricfield.Onethenseesclearlyhowspaceandtimegetmoreandmorestructure,untilfinallyallwehavetodoisdeduceEinstein’sfie
4、ldequations.ThesenotesmaterializedwhenIwasaskedtopresentsomelecturesonGeneralRelativity.Smallchangesweremadeovertheyears.Idecidedtomakethemfreelyavailableontheweb,viamyhomepage.Somereadersexpressedtheirirritationoverthefactthatafter12pagesIswitchnotation:theiinthetime
5、componentsofvectorsdisappears,andthemetricbecomesthe¡+++metric.Whythis“inconsistency”inthenotation?Thereweretworeasonsforthis.Thetransitionismadewhereweproceedfromspecialrelativitytogeneralrelativity.Inspecialrelativity,theihasaconsiderablepracticaladvantage:Lorentztr
6、ansformationsareorthogonal,andallinnerproductsonlycomewith+signs.Noconfusionoversignsremain.Theuseofa¡+++metric,orworseeven,a+¡¡¡metric,inevitablyleadstosignerrors.Ingeneralrelativity,however,theiissuperfluous.Here,weneedtoworkwiththequantityg00anyway.Choosingittobeneg
7、ativerarelyleadstosignerrorsorotherproblems.Butthereisanotherpedagogicalpoint.Iseenoreasontoshieldstudentsagainstthephenomenonofchangesofconventionandnotation.Suchtransitionsarenecessarywheneveroneswitchesfromonefieldofresearchtoanother.Theybettergetusedtoit.Asforappli
8、cationsofthetheory,theusualonessuchasthegravitationalredshift,theSchwarzschildmetric,theperihelionshiftandlightdeflectionarep
