lambourne,relativity, gravitation and cosmology

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1、ContentsRELATIVITY,GRAVITATIONANDCOSMOLOGYIntroduction9Chapter1Specialrelativityandspacetime11Introduction111.1Basicconceptsofspecialrelativity121.1.1Events,framesofreferenceandobservers121.1.2Thepostulatesofspecialrelativity141.2Coordinatetransformations161.2.1TheGalileantransformation

2、s161.2.2TheLorentztransformations181.2.3AderivationoftheLorentztransformations211.2.4Intervalsandtheirtransformationrules231.3ConsequencesoftheLorentztransformations241.3.1Timedilation241.3.2Lengthcontraction261.3.3Therelativityofsimultaneity271.3.4TheDopplereffect281.3.5Thevelocitytran

3、sformation291.4Minkowskispacetime311.4.1Spacetimediagrams,lightconesandcausality311.4.2SpacetimeseparationandtheMinkowskimetric351.4.3Thetwineffect38Chapter2Specialrelativityandphysicallaws45Introduction452.1Invariantsandphysicallaws462.1.1Theinvarianceofphysicalquantities462.1.2Theinva

4、rianceofphysicallaws472.2Thelawsofmechanics492.2.1Relativisticmomentum492.2.2Relativistickineticenergy522.2.3Totalrelativisticenergyandmassenergy542.2.4Four-momentum562.2.5Theenergy–momentumrelation582.2.6Theconservationofenergyandmomentum602.2.7Four-force612.2.8Four-vectors622.3Thelaws

5、ofelectromagnetism675Contents2.3.1Theconservationofcharge672.3.2TheLorentzforcelaw682.3.3Thetransformationofelectricandmagneticfields732.3.4TheMaxwellequations742.3.5Four-tensors75Chapter3Geometryandcurvedspacetime80Introduction803.1Lineelementsanddifferentialgeometry823.1.1Lineelementsi

6、naplane823.1.2Curvedsurfaces853.2Metricsandconnections903.2.1MetricsandRiemanniangeometry903.2.2Connectionsandparalleltransport923.3Geodesics973.3.1Mostdirectroutebetweentwopoints973.3.2Shortestdistancebetweentwopoints983.4Curvature1003.4.1Curvatureofacurveinaplane1013.4.2Gaussiancurvat

7、ureofatwo-dimensionalsurface1023.4.3Curvatureinspacesofhigherdimensions1043.4.4Curvatureofspacetime106Chapter4Generalrelativityandgravitation110Introduction1104.1Thefoundingprinciplesofgeneralrelativity1114.1.1Theprincipleofequivalence1124.1.2Theprincipleofgeneralcovariance1164