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1、Kaluza-KleinGravityJ.M.OverduinDepartmentofPhysicsandAstronomy,UniversityofVictoria,P.O.Box3055,Victoria,BritishColumbia,Canada,V8W3P6andP.S.WessonDepartmentofPhysics,UniversityofWaterloo,Ontario,CanadaN2L3G1andGravityProbe-B,HansenPhysicsLaboratories,StanfordUnivers
2、ity,Stanford,California,U.S.A.94305AbstractWereviewhigher-dimensionaluni edtheoriesfromthegeneralrelativity,ratherthantheparticlephysicsside.Threedistinctapproachestothesubjectareidenti- edandcontrasted:compacti ed,projectiveandnoncompacti ed.Wediscussthecosmological
3、andastrophysicalimplicationsofextradimensions,andconcludethatnoneofthethreeapproachescanberuledoutonobservationalgroundsatthepresenttime.arXiv:gr-qc/9805018v17May1998PreprintsubmittedtoElsevierPreprint20April20011IntroductionKaluza's[1]achievementwastoshowthat ve-dim
4、ensionalgeneralrelativitycontainsbothEinstein'sfour-dimensionaltheoryofgravityandMaxwell'sthe-oryofelectromagnetism.Hehoweverimposedasomewhatarti cialrestriction(thecylindercondition)onthecoordinates,essentiallybarringthe fthoneapriorifrommakingadirectappearanceinthe
5、lawsofphysics.Klein's[2]con-tributionwastomakethisrestrictionlessarti cialbysuggestingaplausiblephysicalbasisforitincompacti cationofthe fthdimension.Thisideawasenthusiasticallyreceivedbyuni ed- eldtheorists,andwhenthetimecametoincludethestrongandweakforcesbyextendin
6、gKaluza'smechanismtohigherdimensions,itwasassumedthatthesetoowouldbecompact.Thislineofthinkinghasledthrougheleven-dimensionalsupergravitytheoriesinthe1980stothecurrentfavoritecontendersforapossibletheoryofeverything,"ten-dimensionalsuperstrings.Wereviewthe eldofKalu
7、za-Kleingravity,concentratingonthegeneralrel-ativity,ratherthanparticlephysicssideofthesubject.(Forthelattertherearealreadymanyexcellentbooks[3{8]andreviewarticles[9{14]available.)Wealsoaimtore-examinethe eldtosomeextent,asitseemstousthatthecartofcompacti cationhasin
8、somewaysgottenaheadofthehorseofuni -cation.Kaluzauni ednotonlygravityandelectromagnetism,butalsomatterandgeometry,forthephotonappea
