General relativity and the pioneers anomaly / Marcelo Samuel Berman.

Format:

Book

Author/Creator:

Berman, Marcelo Samuel.

Series:

Physics research and technology.

Mathematics research developments series.

Physics research and technology

Mathematics research developments

Language:

English

Subjects (All):

General relativity (Physics).

Acceleration (Mechanics).

Relativistic quantum theory.

Physical Description:

1 online resource (221 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2012.

Language Note:

English

Summary:

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)

Contents:

Intro

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

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

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

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.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [181]-200) and index.

Description based on print version record.

ISBN:

1-62100-107-5

OCLC:

831664551