Table Of ContentSergeiM.Kopeikin(Ed.)
FrontiersinRelativisticCelestialMechanics
De Gruyter Studies in
Mathematical Physics
|
Editedby
MichaelEfroimsky,Bethesda,Maryland,USA
LeonardGamberg,Reading,Pennsylvania,USA
DmitryGitman,SãoPaulo,Brazil
AlexanderLazarian,Madison,Wisconsin,USA
BorisSmirnov,Moscow,Russia
Volume 21
Frontiers in Relativistic
Celestial Mechanics
|
Volume 1: Theory
Edited by
Sergei M. Kopeikin
PhysicsandAstronomyClassificationScheme2010
04.20.-q,04.25.-g,04.25.Nx,95.10.Ce,95.30.Sf,98.80.Jk
Editor
Prof.Dr.SergeiM.Kopeikin
UniversityofMissouri
DepartmentofPhysics&Astronomy
223PhysicsBldg.
Columbia,MO65211
USA
E-mail:[email protected]
ISBN978-3-11-033747-1
e-ISBN978-3-11-033749-5
Set-ISBN978-3-11-035932-9
ISSN2194-3532
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ThisFestschriftisdedicatedtoProfessorVictorA.Brumberg,
forhisenthusiasmanddevotiontothescienceofrelativisticcelestialmechanics,
andtocelebratehis80thbirthday.
List of contributors
Prof.Dr.ThibaultDamour Prof.Dr.MichaelSoffel
InstituteofAdvancedScientificStudies(IHÉS) DresdenUniversityofTechnology
35routedeChartres LohrmannObservatoryTUDresden
BuressurYvette,F-91440 PlanetaryGeodesy
France Mommsenstr13
E-mail:[email protected] 01062Dresden
Germany
Prof.Dr.ToshifumiFutamase
E-mail:[email protected]
TohokuUniversity
AstronomicalInstitute Dr.PavelKorobkov
Sendai980-8578 SolovetskyMonastery
Japan ArkhangelskRegion164070
E-mail:[email protected] Russia
Prof.Dr.SergeiKopeikin Dr.AlexanderPetrov
UniversityofMissouri MoscowLomonosovStateUniversity
DepartmentofPhysics&Astronomy SternbergAstronomicalInstitute
223PhysicsBldg. UniversitetskiyProspect13
Columbia,MO65211 Moscow119992
USA Russia
E-mail:[email protected] E-mail:[email protected]
Prof.Dr.GerhardSchäfer Dr.XieYi
FriedrichSchillerUniversityJena NanjingUniversity
InstituteofTheoreticalPhysics DepartmentofAstronomy
Max-Wien-Platz1 22HankouRoad
D-07743Jena NanjingJiangsu210093
Germany P.R.China
E-mail:[email protected] E-mail:[email protected]
Contents
Listoffigures|xii
Preface|xiii
ThibaultDamour
Thegeneralrelativistictwo-bodyproblem|1
1 Introduction|1
2 Multichartapproachtothe -bodyproblem|4
𝑁
3 EOBdescriptionoftheconservativedynamicsoftwo-body
systems|6
4 EOBdescriptionofradiationreactionandoftheemittedwaveform
duringinspiral|15
5 EOBdescriptionofthemergerofbinaryblackholesandoftheringdown
ofthefinalblackhole|20
6 EOBvsNR|23
6.1 EOB[NR]waveformsvsNRones|23
6.2 EOB[3PN]dynamicsvsNRone|26
7 Otherdevelopments|28
7.1 EOBwithspinningbodies|28
7.2 EOBwithtidallydeformedbodies|29
7.3 EOBandGSF|29
8 Conclusions|31
References|31
GerhardSchäfer
Hamiltoniandynamicsofspinningcompactbinariesthroughhighpost-Newtonian
approximations|39
1 Introduction|39
2 Hamiltonianformulationofgeneralrelativity|40
2.1 Pointparticles|43
2.2 Spinningparticles|44
2.3 IntroducingtheRouthian|45
3 ThePoincaréalgebra|46
4 Post-NewtonianbinaryHamiltonians|47
4.1 Spinlessbinaries|47
4.2 Spinningbinaries|50
5 Binarymotion|53
5.1 Spinlesstwo-bodysystems|53
5.2 ParticlemotioninKerrgeometry|57
viii | Contents
5.3 Two-bodysystemswithspinningcomponents|61
References|62
YiXieandSergeiKopeikin
Covarianttheoryofthepost-Newtonianequationsofmotionofextended
bodies|65
1 Introduction|65
2 Atheoryofgravityforpost-Newtoniancelestialmechanics|71
2.1 Thefieldequations|72
2.2 Theenergy–momentumtensor|73
3 Parameterizedpost-Newtoniancelestialmechanics|74
3.1 Externalandinternalproblemsofmotion|75
3.2 Solvingthefieldequationsbypost-Newtonianapproximations|77
3.3 Thepost-Newtonianfieldequations|81
3.4 Conformalharmonicgauge|84
4 Parameterizedpost-Newtoniancoordinates|85
4.1 Theglobalpost-Newtoniancoordinates|86
4.2 Thelocalpost-Newtoniancoordinates|90
5 Post-Newtoniancoordinatetransformationsbyasymptotic
matching|100
5.1 Generalstructureofthetransformation|100
5.2 Matchingsolution|105
6 Post-Newtonianequationsofmotionofextendedbodiesinlocal
coordinates|110
6.1 Microscopicpost-Newtonianequationsofmotion|110
6.2 Post-Newtonianmassofanextendedbody|111
6.3 Post-Newtoniancenterofmassandlinearmomentumofanextended
body|113
6.4 Translationalequationofmotioninthelocalcoordinates|115
7 Post-Newtonianequationsofmotionofextendedbodiesinglobal
coordinates|118
7.1 STFexpansionsoftheexternalgravitationalpotentialsintermsofthe
internalmultipoles|118
7.2 Translationalequationsofmotion|123
8 Covariantequationsoftranslationalmotionofextendedbodies|135
8.1 Effectivebackgroundmanifold|135
8.2 Geodesicmotionand4-force|137
8.3 Four-dimensionalformofmultipolemoments|139
8.4 Covarianttranslationalequationsofmotion|142
8.5 ComparisonwithDixon’stranslationalequationsofmotion|147
References|147
Contents | ix
MichaelSoffel
OntheDSX-framework|155
1 Introduction|155
2 Thepost-Newtonianformalism|159
2.1 Thegeneralformofthemetric|159
3 Fieldequationsandthegaugeproblem|163
4 Thegravitationalfieldofabody|166
4.1 Post-Newtonianmultipolemoments|166
5 GeodesicmotioninthePN-Schwarzschildfield|169
6 Astronomicalreferenceframes|174
6.1 Transformationbetweenglobalandlocalsystems:firstresults|174
6.2 Splitoflocalpotentials,multipolemoments|177
6.3 Tetradinducedlocalcoordinates|179
6.4 Thestandardtransformationbetweenglobal
andlocalcoordinates|180
6.5 Thedescriptionoftidalforces|183
7 Thegravitational -bodyproblem|186
𝑁
7.1 Localevolutionequations|186
7.2 Thetranslationalmotion|188
8 Furtherdevelopments|190
References|191
PavelKorobkovandSergeiKopeikin
Generalrelativistictheoryoflightpropagationinmultipolargravitational
fields|195
1 Introduction|195
1.1 Statementoftheproblem|195
1.2 Historicalbackground|199
1.3 Notationsandconventions|202
2 Themetrictensor,gaugesandcoordinates|206
2.1 Thecanonicalformofthemetrictensorperturbation|206
2.2 Theharmoniccoordinates|209
2.3 TheADMcoordinates|211
3 Equationsofpropagationofelectromagneticsignals|213
3.1 Maxwellequationsincurvedspacetime|213
3.2 Maxwellequationsinthegeometricopticsapproximation|214
3.3 Electromagneticeikonalandlight-raygeodesics|215
3.4 PolarizationoflightandtheStokesparameters|226
4 Mathematicaltechniqueforanalyticintegration
oflight-rayequations|236
4.1 Monopoleanddipolelight-rayintegrals|236
x | Contents
4.2 Light-rayintegralsfromquadrupoleandhigherorder
multipoles|238
5 Gravitationalperturbationsofthelightray|242
5.1 Relativisticperturbationoftheelectromagneticeikonal|242
5.2 Relativisticperturbationofthecoordinatevelocityoflight|245
5.3 Perturbationofthelight-raytrajectory|247
6 Observablerelativisticeffects|251
6.1 Gravitationaltimedelayoflight|251
6.2 Gravitationaldeflectionoflight|253
6.3 Gravitationalshiftoffrequency|257
6.4 Gravity-inducedrotationoftheplaneofpolarizationoflight|263
7 Lightpropagationthroughthefieldofgravitationallens|267
7.1 Smallparametersandasymptoticexpansions|268
7.2 Asymptoticexpressionsforobservableeffects|271
8 Lightpropagationthroughthefieldofplanegravitational
waves|273
8.1 Plane-waveasymptoticexpansions|273
8.2 Asymptoticexpressionsforobservableeffects|276
References|278
ToshifumiFutamase
Onthebackreactionproblemincosmology|283
1 Introduction|283
2 Formulationandaveraging|285
3 CalculationintheNewtoniangauge|287
4 Definitionofthebackground|289
5 Conclusions|292
References|293
AlexanderPetrovandSergeiKopeikin
Post-Newtonianapproximationsincosmology|295
1 Introduction|295
2 Derivativesonthegeometricmanifold|305
2.1 Variationalderivative|305
2.2 Liederivative|308
3 Lagrangianandfieldvariables|309
3.1 Actionfunctional|310
3.2 Lagrangianoftheidealfluid|311
3.3 Lagrangianofscalarfield|313
3.4 Lagrangianofalocalizedastronomicalsystem|315
4 Backgroundmanifold|315
4.1 Hubbleflow|315
