08534nam 2200673 a 450 991096213860332120251116181931.01-62100-107-5(CKB)2550000001043908(EBL)3021888(SSID)ssj0000874930(PQKBManifestationID)12301696(PQKBTitleCode)TC0000874930(PQKBWorkID)10887390(PQKB)11269093(MiAaPQ)EBC3021888(Au-PeEL)EBL3021888(CaPaEBR)ebr10686211(OCoLC)831664551(BIP)35435273(BIP)35435271(EXLCZ)99255000000104390820110815d2012 uy 0engur|n|---|||||txtccrGeneral relativity and the pioneers anomaly /Marcelo Samuel Berman1st ed.New York Nova Science Publishersc20121 online resource (221 p.)Physics research and technologyMathematics research developmentsDescription based upon print version of record.1-62100-003-6 Includes bibliographical references (p. [181]-200) and index.Intro -- GENERAL RELATIVITY AND THE PIONEERS ANOMALY -- GENERAL RELATIVITY AND THE PIONEERS ANOMALY -- Contents -- Preface and Introduction -- Part I MATHEMATICAL PRELIMINARIES -- Tensors in Amorphous Spaces -- 1.1.Introduction -- 1.2.VectorsandTensors -- ContravariantVectors -- ContravariantTensorsof2NDRank -- CovariantVectors -- CovariantTensorsof2ndRank -- MixedTensors -- SolvedProblem -- 1.3.AlgebraicOperationswithTensors -- ExteriorProduct -- Contraction -- InteriorProduct -- TestsofTensorCharacter -- 1.4.FinalObservations -- ReferencesforChapter1 -- Tensors in Riemann Spaces -- 2.1.Metric -- ContravariantMetricTensor -- 2.2.ChristoffelSymbols -- 2.3.CovariantDerivative -- 2.4.CurvatureTensors -- RicciTensor -- RicciScalarCurvature -- Einstein'sTensor -- GeodesicCoordinateSystem -- BianchiIdentity -- ReferencesforFurtherStudy -- Part II INTRODUCTION TO GENERAL RELATIVITY -- Basic Theory -- 3.1.TheBasicPrinciples -- 3.2.Energy-MomentumTensor -- 1st)ContinuityEquation. -- 2nd)Euler'sequation. -- 3.3.TijfortheElectromagneticField -- 3.4.Einstein'sFieldEquations -- 3.5.IntroducingtheCosmologicalConstant -- 3.6.ReductionofGRTintoNewtonianPhysics -- 3.7.TheGeodesicsEquation-aDerivation -- 3.8.GravitationalRadiation -- Schwarzschild's Metric and Classical Experimental Tests -- 4.1.SphericallySymmetricMetrics -- 4.2.TheMotionofPlanetsandPerihelionPrecession -- 4.3.PropagationofLightnearGravitationalFields -- 4.4.SpectralDisplacementduetoGravitationalCause -- 4.5.OtherVerificationsoftheGRT -- 1st)Gravitomagnetismandgalacticrotations -- 2nd)Hafele-Keatingexperiment: -- 3rd)Shapiroexperiment: -- 4th)Hulse-Taylorobservations: -- 5th)GlobalPositioningSystem(GPS)-NAVSTAR: -- FinalComments -- Complements of Tensor Calculus and General Relativity (Optional Study) -- 5.1.OrthogonalTransformationsandCartesianTensors -- CartesianTensors.5.2.ParallelTransportinRiemannSpace -- 5.3.Fermi-Walker'sTransport -- 5.4.LieDerivative -- 5.5.Isometries -- 5.6.StationaryandStaticFields -- StaticField -- MathematicalNote. -- Part III INTRODUCTION TO RELATIVISTIC COSMOLOGY -- Digression into Philosophical and Mathematical Matters (Optional Study) -- 6.1.NewtonianConceptsofSpaceandTime -- 6.2.ObjectionstoNewton'sCosmology -- 6.3.Mach'sPrinciple -- 6.4.ThePotentialforGravitation -- 6.5.EquivalencePrinciple -- 6.6.Theprinciplesof(General)Relativity,Covariance,andSimplicity -- 6.7.Principlesof"cosmictime"and"correspondence" -- FinalObservations: -- 6.8.RevisitingMach'sPrinciple -- Introductory Cosmological Models -- 7.1.DerivationoftheHomogeneousandIsotropicMetric -- 7.2.Einstein'sFieldEquationsforCosmology -- 7.3.ConstantDecelerationParameterModels -- 7.4.CosmologicalRed-Shift -- 7.5.Hubble'sLaw -- 7.6.CosmologicalModelforLargeLambda -- 7.7.Inflation -- 7.8.Planck'sUniverseandtheL-problem -- 7.9.Raychaudhuri'sEquationandanAlternativeForm -- 7.10.GeodesicsforPhotons,Particles,andTachyonsinRobertson-Walker'sCosmology -- IntroductiontotheProblem -- NullGeodesics -- GeodesicsforParticlesandTachyonsinaflatUniverse -- 7.11.EnergyofRobertson-Walker'sUniverse -- 7.12.TheZero-TotalEnergyDensityoftheUniverse -- 7.13.TheCosmologicalNewtonianLimitofGeneralRelativity -- Part IV THE PIONEERS ANOMALY -- The Pioneers Anomaly and a Machian Universe -- 8.1.BriefHistoryofthePioneersAnomaly -- 8.2.TheZero-TotalEnergyMachianUniverse -- APPLICATION1-THEPIONEERSANOMALIES -- APPLICATION2-MAGNETICFIELDOFTHEUNIVERSE -- APPLICATION3-TIME-VARYINGNEUTRINOMASS -- Atheoryforneutrinosenergydensity -- APPLICATION4-AREMASSANDLENGTHQUANTIZED? -- Macromassandmicromass -- Quantizationofgeometry -- RemovalofinitialsingularityinCosmology -- 8.3.Dirac'sLNHwithTime-VaryingFundamental"Constants" -- POWER-LAWVARIATIONS -- EXPONENTIALINFLATION.ROTATIONOFTHEUNIVERSE -- PROSANDCONSOFTHEPRESENTCALCULATIONS -- 8.4.OnSciama'sMachianOriginofInertia -- SCIAMA'SINERTIAMODEL -- GRANEAUANDGRANEAU'STHEORY -- 8.5.Sciama'sMachianUniverse -- ONBERRY'SMACHIANARGUMENT -- GRAVITATIONALRADIATIONINSCIAMA'SMACHIANMODEL -- QUADRUPOLEANDDIPOLERADIATION -- TEMPERATUREOFTHEUNIVERSE.ENTROPY -- CONCLUSIONS -- 8.6.ExactBrans-DickeRelationandVariableSpeedofLight -- PIONEERSANOMALYSOLUTION -- CONCLUSIONS -- Relativistic Cosmology and the Pioneers Anomaly -- 9.1.GeneralisedRobertson-Walker'sMetric:RotationPlusEx-pansion -- ZERO-TOTALENERGY-DENSITYOFTHEROTATINGEVOLUTIONARYUNIVERSE -- 9.2.GeneralisedRobertson-Walker'sMetric:RotationPlusEx-pansion-II -- ROTATINGEVOLUTIONARYMETRICS -- GENERALISEDGAUSSIANMETRICS -- SOMECOMMENTS -- 9.3.ThePioneersAnomalyandaMachianGeneralRelativisticModel -- ENERGYOFTHEROTATINGEVOLUTIONARYUNIVERSE -- ANALTERNATIVEDERIVATION -- PIONEERSANOMALYREVISITED -- SOMECOMMENTSANDDISCUSSION -- 9.4.GeneralRelativisticCosmologicalModelswithPioneersAnomaly -- ANEXACTSOLUTIONTOTHEPIONEERSANOMALY -- CONCLUSIONS -- 9.5.TheFundamentalTheoremforthePioneersAnomalySo-lutioninGeneralRelativity -- 9.6.ThePioneersAnomalySolutionwithUniversalSpinCon-servationinGeneralRelativity -- The Pioneers Anomaly and Several Relativistic Theories -- 10.1.OnSchwarzschild'sandRobertson-Walker´sModels -- CLASSICALORIGINFORTHEDARKENERGY -- CONCLUSIONSANDPREDICTIONS -- 10.2.LinearizedGravitomagnetismandPioneersAnomaly -- GENERALRELATIVISTICLINEARPERTURBATIONAPPROACH -- ENERGYDENSITYOFTHEROTATINGUNIVERSE -- 10.3.ThePioneersAnomalyinaVariableSpeedofLightRela-tivisticCosmology -- FIELDEQUATIONSANDCONSTANTDECELERATIONSOLUTION -- PIONEERSANOMALYSOLUTION -- 10.4.EnergyandStabilityofOurUniverse -- THEZERO-TOTALENERGYOFTHEROTATINGEVOLUTIONARYUNI-VERSE -- STABILITYOFOURUNIVERSE -- 10.5.Frame-Dragging,Mach.sPrinciple,andthePioneersAnomalies.10.6.GravitationalLarmorTheoremandthePioneersAnomaly -- Possible Solutions to the Pioneers Anomaly -- 11.1.EvidenceontheRotationoftheUniverse -- 11.2.ThermalEmissionasDecelerationCause -- 11.3.MOND(ModifiedNewtonianDynamics)byMilgrom -- 11.4.OtherExplanations -- 11.5.ConcludingRemarks -- Part V BIBLIOGRAPHY AND REFERENCES -- Bibliography and References -- INDEX.This book is an introduction to the General Relativity Theory (GRT) and to the solution of the Pioneers Anomaly by means of relativistic cosmology, a study that is designed to be understood by undergraduate and graduate students alike in the fields of theoretical physics, applied mathematics and space engineering. In fact, this book is the first elementary account of GRT and cosmology to address the NASA problem, which consists of a specific deceleration suffered by two space-probes launched to outer space more than thirty years ago. (Imprint: Nova)Physics research and technology.Mathematics research developments series.General relativity (Physics)Acceleration (Mechanics)Relativistic quantum theoryGeneral relativity (Physics)Acceleration (Mechanics)Relativistic quantum theory.530.11Berman Marcelo Samuel1862756MiAaPQMiAaPQMiAaPQBOOK9910962138603321General relativity and the pioneers anomaly4475018UNINA