general relativity and cosmology for undergraduates - j. norbury

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1、GENERALRELATIVITY&COSMOLOGYforUndergraduatesProfessorJohnW.NorburyPhysicsDepartmentUniversityofWisconsin-MilwaukeeP.O.Box413Milwaukee,WI532011997Contents1NEWTONIANCOSMOLOGY51.1Introduction............................51.2EquationofState......................

2、...51.2.1Matter...........................61.2.2Radiation.........................61.3VelocityandAccelerationEquations..............71.4CosmologicalConstant......................91.4.1EinsteinStaticUniverse.................112APPLICATIONS132.1Conservationla

3、ws........................132.2AgeoftheUniverse.......................142.3In°ation..............................152.4QuantumCosmology.......................162.4.1DerivationoftheSchrÄodingerequation.........162.4.2Wheeler-DeWittequation................172.

4、5Summary.............................182.6Problems.............................192.7Answers..............................202.8Solutions.............................213TENSORS233.1ContravariantandCovariantVectors..............233.2HigherRankTensors..........

5、.............263.3ReviewofCartesianTensors...................273.4MetricTensor...........................283.4.1SpecialRelativity.....................303.5Christo®elSymbols........................3112CONTENTS3.6Christo®elSymbolsandMetricTensor.............3

6、63.7RiemannCurvatureTensor...................383.8Summary.............................393.9Problems.............................403.10Answers..............................413.11Solutions.............................424ENERGY-MOMENTUMTENSOR454.1Euler-Lagrang

7、eandHamilton'sEquations...........454.2ClassicalFieldTheory......................474.2.1ClassicalKlein-GordonField..............484.3PrincipleofLeastAction....................494.4Energy-MomentumTensorforPerfectFluid..........494.5ContinuityEquation........

8、...............514.6InteractingScalarField.....................514.7CosmologywiththeScalarField................534.7.1Alternativederivation..................554.7.2Limitingsolutions....................