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1、Abstract:Thisarticle—summarizingtheauthors’thennovelformulationofGeneralRelativity—appearedasChapter7,pp.227–264,inGravitation:anintroductiontocurrentresearch,L.Witten,ed.(Wiley,NewYork,1962),nowlongoutofprint.Intentionallyunretouched,thispostingisintendedtoprovidecontemporar
2、yaccessibilitytotheflavoroftheoriginalideas.Sometypographicalcorrectionshavebeenmade:footnoteandpagenumberinghavechanged—butnotsectionnorequationnumbering,etc.Currentinstitutionalaffiliationsareencodedin:arnowitt@physics.tamu.edu,deser@brandeis.edu,mis-ner@physics.umd.edu.R.Arno
3、witt,iS.Deser,iiandC.W.MisneriiiTheDynamicsofGeneralRelativity1.IntroductionivThegeneralcoordinateinvarianceunderlyingthetheoryofrelativitycreatesbasicproblemsintheanalysisofthedynamicsofthegravitationalfield.Usually,specificationofthefieldamplitudesandtheirfirsttimederivativesin
4、itiallyisappropriatetodeterminethetimedevelopmentofafieldviewedasadynamicalentity.Forgeneralrelativity,however,themetricfieldgµνmaybemodifiedarXiv:gr-qc/0405109v119May2004atanylatertimesimplybycarryingoutageneralcoordinatetransformation.Suchanoperationdoesnotinvolveanyobservable
5、changesinthephysics,sinceitmerelycorrespondstoarelabelingunderwhichthetheoryisinvariant.Thusitisnecessarythatthemetricfieldbeseparatedintothepartscarryingthetruedynamicalinformationandthosepartscharacterizingthecoordinatesystem.Inthisrespect,thegeneraltheoryisanalogoustoelectr
6、omagnetictheory.Inparticular,thecoordinateinvarianceplaysarolesimilartothegaugeinvarianceoftheMaxwellfield.Inthelattercase,thisgaugeinvariancealsoproducesdifficultiesinseparatingouttheindependentdynamicalmodes,althoughthelinearityheredoessimplifytheanalysis.Inbothcases,theeffecti
7、PhysicsDepartment,SyracuseUniversity,Syracuse,NY.(ResearchsupportedinpartbytheNationalScienceFoundationandtheUnitedStatesAirForce—AeronauticalResearchLaboratory,WADD,andOfficeofScientificResearch.)iiPhysicsDepartment,BrandeisUniversity,Waltham,MA.(ResearchsupportedinpartbytheNat
8、ionalScienceFoundationandtheUnitedStatesAirForceOfficeofScientificResea
