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1、SpecialTheoryofRelativityonCurvedSpace-timeMoninderSinghModgilDepartmentofPhysics,IndianInstituteofTechnology,Kanpur,IndiaEmail:msingh@iitk.ac.inDate:16August20041SpecialTheoryofRelativityonCurvedSpace-timeAbstractSpace-timemeasurements,ofgedankenexperimentsofspecialrelativityne
2、edmodificationincurvedspaces-times.Itisfoundthatinaspace-timewithmetricg,the1µspecialrelativisticfactorg,hastobereplacedbyg=,whereV=(1,v,0,0),gmngVVmnisthe4-velocity,andvtherelativevelocitybetweenthetwoframesExamplesaregivenforSchwarzschildmetric,Freidmann-Robertson-Walkermetric
3、,andtheGödelmetric.Amongthenoveltiesareparadoxicaltachyonicstates,withgbecomingimaginary,forgvelocitieslessthanthatoflight,duetospace-timecurvature.Relativisticmassbecomesamnµfunctionofspace-timecurvature,m=gPP,whereP=(E,p)isthe4-momentum,mnsignalinganewformofMach’sprinciple,inw
4、hichaglobalobject–namelythemetrictensor,iseffectinginteria.PACS:03.30.+p,042SpecialTheoryofRelativityonCurvedSpace-time1.IntroductionItisgenerallyconsideredthatthelawsofphysicscanlocallybedescribedinaflatspace-timesetting.Thisisdescribedbythestatementthatlocallyanyspace-timeisMi
5、nkowskian.However,space-timecurvaturecansignificantlyeffectlocalphysics.OneexampleofthisistheHawkingradiation[1].Anotherexampleistheeffectofaccelerationonreadingofparticledetectorsincurvedspace-times[2].Space-timecurvatureeffectslocalstructureoflightcone,andthebehaviourofnullgeo
6、desics.SincegedankenexperimentsofSpecialTheoryofrelativity(STR)arebaseduponpropagationoflightsignals,therefore.itmaybeenquired,howwouldthevariousresultsofSTRgetmodified,whenthespace-timeiscurved.Specialtheoryofrelativity(STR)isbasedupontheMinkowskimetric,2mnds=hdxdx,m,n=0,1,2,3(
7、1)mnInacurvedspace-timewiththelineelement,2mnds=gdxdx,(2)mneffectoflocalcurvature,intheformofcomponentsofmetrictensor,gmaybemnexpectedtoshowupinthelocalmeasurements.Thelineelementofanullgeodesicinbothflatandcurvedspace-timesischaracterizedby,2ds=0.(3)3Thisequationsencodesthefund
8、amentalprincipleofSTR,namelytheconstancyofspeed
