intro to differential geometry and general relativity - s. waner

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1、IntroductiontoDifferentialGeometry&GeneralRelativity4thPrintingJanuary2005LectureNotesbyStefanWanerwithaSpecialGuestLecturebyGregoryC.LevineDepartmentsofMathematicsandPhysics,HofstraUniversityIntroductiontoDifferentialGeometryandGeneralRelativityLecture

2、NotesbyStefanWaner,withaSpecialGuestLecturebyGregoryC.LevineDepartmentofMathematics,HofstraUniversityThesenotesarededicatedtothememoryofHannoRund.TABLEOFCONTENTS1.Preliminaries.............................................................................

3、.........................32.SmoothManifoldsandScalarFields..............................................................73.TangentVectorsandtheTangentSpace.......................................................144.ContravariantandCovariantVectorFields..

4、..............................................245.TensorFields....................................................................................................356.RiemannianManifolds....................................................................

5、...............407.LocallyMinkowskianManifolds:AnIntroductiontoRelativity.............508.CovariantDifferentiation...............................................................................619.GeodesicsandLocalInertialFrames.........................

6、....................................6910.TheRiemannCurvatureTensor..................................................................8211.ALittleMoreRelativity:ComovingFramesandProperTime...............9412.TheStressTensorandtheRelativisticStress-EnergyT

7、ensor................10013.TwoBasicPremisesofGeneralRelativity................................................10914.TheEinsteinFieldEquationsandDerivationofNewton'sLaw...........11415.TheSchwarzschildMetricandEventHorizons...............................

8、.......12416.WhiteDwarfs,NeutronStarsandBlackHoles,byGregoryC.Levine131ReferencesandFurtherReading................................................................13821.PreliminariesDistanceandOpenSetsHere,wedojustenoughtopologyso