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1、Kaluza-KleinGravityJ.M.OverduinDepartmentofPhysicsandAstronomy,UniversityofVictoria,P.O.Box3055,Victoria,BritishColumbia,Canada,V8W3P6andP.S.WessonDepartmentofPhysics,UniversityofWaterloo,Ontario,CanadaN2L3G1andGravityProbe-B,HansenPhysicsLaboratories,StanfordUniversity,Stanford,Ca
2、lifornia,U.S.A.94305AbstractWereviewhigher-dimensionaluni edtheoriesfromthegeneralrelativity,ratherthantheparticlephysicsside.Threedistinctapproachestothesubjectareidenti- edandcontrasted:compacti ed,projectiveandnoncompacti ed.Wediscussthecosmologicalandastrophysicalimplicationsof
3、extradimensions,andconcludethatnoneofthethreeapproachescanberuledoutonobservationalgroundsatthepresenttime.arXiv:gr-qc/9805018v17May1998PreprintsubmittedtoElsevierPreprint20April20011IntroductionKaluza's[1]achievementwastoshowthat ve-dimensionalgeneralrelativitycontainsbothEinstein
4、'sfour-dimensionaltheoryofgravityandMaxwell'sthe-oryofelectromagnetism.Hehoweverimposedasomewhatarti cialrestriction(thecylindercondition)onthecoordinates,essentiallybarringthe fthoneapriorifrommakingadirectappearanceinthelawsofphysics.Klein's[2]con-tributionwastomakethisrestrictio
5、nlessarti cialbysuggestingaplausiblephysicalbasisforitincompacti cationofthe fthdimension.Thisideawasenthusiasticallyreceivedbyuni ed- eldtheorists,andwhenthetimecametoincludethestrongandweakforcesbyextendingKaluza'smechanismtohigherdimensions,itwasassumedthatthesetoowouldbecompact
6、.Thislineofthinkinghasledthrougheleven-dimensionalsupergravitytheoriesinthe1980stothecurrentfavoritecontendersforapossibletheoryofeverything,"ten-dimensionalsuperstrings.Wereviewthe eldofKaluza-Kleingravity,concentratingonthegeneralrel-ativity,ratherthanparticlephysicssideofthesub
7、ject.(Forthelattertherearealreadymanyexcellentbooks[3{8]andreviewarticles[9{14]available.)Wealsoaimtore-examinethe eldtosomeextent,asitseemstousthatthecartofcompacti cationhasinsomewaysgottenaheadofthehorseofuni -cation.Kaluzauni ednotonlygravityandelectromagnetism,butalsomatterand
8、geometry,forthephotonappea
