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Gravitational waves PDF

422 Pages·2001·2.763 MB·English
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GRAVITATIONALWAVES Series inHighEnergy Physics,CosmologyandGravitation Otherbooksintheseries Electron–PositronPhysicsattheZ MGGreen,SLLloyd,PNRatoffandDRWard Non-acceleratorParticlePhysics Paperbackedition HVKlapdor-KleingrothausandAStaudt IdeasandMethodsofSupersymmetryandSupergravity orAWalkThroughSuperspace Revisededition ILBuchbinderandSMKuzenko PulsarsasAstrophysicalLaboratoriesforNuclearandParticlePhysics FWeber ClassicalandQuantumBlackHoles EditedbyPFre´,VGorini,GMagliandUMoschella ParticleAstrophysics Revisedpaperbackedition HVKlapdor-KleingrothausandKZuber TheWorldinElevenDimensions Supergravity,SupermembranesandM-Theory EditedbyMJDuff GRAVITATIONAL WAVES Edited by Ignazio Ciufolini DepartmentofEngineering, UniversityofLecce Vittorio Gorini, Ugo Moschella DepartmentofChemical,MathematicalandPhysicalSciences, UniversityofInsubriaatComo and Pietro Fre´ DepartmentofPhysics,UniversityofTurin INSTITUTE OF PHYSICS PUBLISHING BRISTOL AND PHILADELPHIA c IOPPublishingLtd2001 (cid:13) All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical,photocopying,recordingorotherwise,withoutthepriorpermission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreementwiththeCommitteeofVice-ChancellorsandPrincipals. BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN0750307412 LibraryofCongressCataloging-in-PublicationDataareavailable CommissioningEditor:JamesRevill ProductionEditor:SimonLaurenson ProductionControl:SarahPlenty CoverDesign:VictoriaLeBillon MarketingExecutive:ColinFenton Published by Institute of Physics Publishing, wholly owned by The Institute of Physics,London InstituteofPhysicsPublishing,DiracHouse,TempleBack,BristolBS16BE,UK US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035,150SouthIndependenceMallWest,Philadelphia,PA19106,USA TypesetinTEXusingtheIOPBookmakerMacros PrintedintheUKbyMPGBooksLtd,Bodmin Contents Preface xiii 1 Gravitationalwaves,theoryandexperiment(anoverview) 1 References 9 PART1 GravitationalWaves,SourcesandDetectors BernardFSchutzandFrancoRicci 11 Synopsis 13 2 Elementsofgravitationalwaves 15 2.1 Mathematicsoflinearizedtheory 16 2.2 UsingtheTTgaugetounderstandgravitationalwaves 17 2.3 Interactionofgravitationalwaveswithdetectors 19 2.4 Analysisofbeamdetectors 21 2.4.1 Rangingtospacecraft 21 2.4.2 Pulsartiming 22 2.4.3 Interferometry 22 2.5 Exercisesforchapter2 22 3 Gravitational-wavedetectors 24 3.1 Gravitational-waveobservables 26 3.2 Thephysicsofinterferometers 28 3.2.1 Newinterferometersandtheircapabilities 32 3.3 Thephysicsofresonantmassdetectors 34 3.3.1 Newbardetectorsandtheircapabilities 37 3.4 Adetectorinspace 38 3.4.1 LISA’scapabilities 39 3.5 Gravitationalandelectromagneticwavescomparedandcontrasted 41 vi Contents 4 Astrophysicsofgravitational-wavesources 43 4.1 Sourcesdetectablefromgroundandfromspace 43 4.1.1 Supernovaeandgravitationalcollapse 43 4.1.2 Binarystars 44 4.1.3 Chirpingbinarysystems 44 4.1.4 Pulsarsandotherspinningneutronstars 46 4.1.5 Randombackgrounds 48 4.1.6 Theunexpected 49 5 Wavesandenergy 50 5.1 Variationalprincipleforgeneralrelativity 50 5.2 Variationalprinciplesandtheenergyingravitationalwaves 51 5.2.1 Gaugetransformationandinvariance 52 5.2.2 Gravitational-waveaction 52 5.3 PracticalapplicationsoftheIsaacsonenergy 54 5.3.1 Curvatureproducedbywaves 55 5.3.2 Cosmologicalbackgroundofradiation 55 5.3.3 Otherapproaches 56 5.4 Exercisesforchapter5 56 6 Mass-andcurrent-quadrupoleradiation 58 6.1 Expansionforthefarfieldofaslow-motionsource 58 6.2 ApplicationoftheTTgaugetothemassquadrupolefield 60 6.2.1 TheTTgaugetransformations 60 6.2.2 QuadrupolefieldintheTTgauge 61 6.2.3 Radiationpatternsrelatedtothemotionofsources 62 6.3 ApplicationoftheTTgaugetothecurrent-quadrupolefield 64 6.3.1 Thefieldatthirdorderinslow-motion 64 6.3.2 Separatingthecurrentquadrupolefromthemassoctupole 65 6.3.3 Amodelsystemradiatingcurrent-quadrupoleradiation 67 6.4 Energyradiatedingravitationalwaves 68 6.4.1 Mass-quadrupoleradiation 69 6.4.2 Current-quadrupoleradiation 69 6.5 RadiationintheNewtonianlimit 70 7 Sourcecalculations 71 7.1 Radiationfromabinarysystem 71 7.1.1 Corrections 73 7.2 Ther-modes 73 7.2.1 Lineargrowthofther-modes 76 7.2.2 Nonlinearevolutionofthestar 77 7.2.3 Detectionofr-moderadiation 79 7.3 Conclusion 80 References 81 Solutionstoexercises 84 Contents vii PART2 Gravitational-wavedetectors GuidoPizzella,AngelaDiVirgilio,PeterBenderandFrancescoFucito 89 8 Resonantdetectorsforgravitationalwavesandtheirbandwidth 91 8.1 Sensitivityandbandwidthofresonantdetectors 91 8.2 SensitivityforvariousGWsignals 95 8.3 Recentresultsobtainedwiththeresonantdetectors 99 8.4 Discussionandconclusions 101 References 102 9 TheEarth-basedlargeinterferometerVirgoandtheLowFrequency Facility 103 9.1 Introduction 103 9.1.1 InterferometerprinciplesandVirgoparameters 104 9.2 TheSAsuspensionandrequirementsonthecontrol 108 9.3 AfewwordsabouttheLowFrequencyFacility 111 9.4 Conclusion 112 References 114 10 LISA:AproposedjointESA–NASAgravitational-wavemission 115 10.1 DescriptionoftheLISAmission 115 10.1.1 Introduction 115 10.1.2 Overallantennaandspacecraftdesign 116 10.1.3 Opticsandinterferometrysystem 121 10.1.4 Freemasssensors 125 10.1.5 Micronewtonthrusters 129 10.1.6 Missionscenario 131 10.2 Expectedgravitational-waveresultsfromLISA 132 10.2.1 LISAsensitivityandgalacticsources 132 10.2.2 Originofmassiveblackholes 136 10.2.3 Massiveblackholesinnormalgalaxies 138 10.2.4 Structureformationandmassiveblackholecoalescence 141 10.2.5 FundamentalphysicstestswithLISA 143 10.2.6 Futureprospects 146 Acknowledgments 148 References 148 11 Detectionofscalargravitationalwaves 152 11.1 Introduction 152 11.2 Testingtheoriesofgravity 154 11.2.1 Freevibrationsofanelasticsphere 154 11.2.2 Interaction of a metric GW with the sphere vibrational modes 155 11.2.3 Measurements of the sphere vibrations and wave polarizationstates 157 viii Contents 11.3 GravitationalwaveradiationintheJBDtheory 159 11.3.1 ScalarandTensorGWsintheJBDTheory 160 11.3.2 PoweremittedinGWs 161 11.3.3 PoweremittedinscalarGWs 162 11.3.4 ScalarGWs 164 11.3.5 DetectabilityofthescalarGWs 165 11.4 Thehollowsphere 168 11.5 Scalar–tensorcrosssections 170 Acknowledgments 176 References 176 PART3 TheStochasticGravitational-WaveBackground DBabusci,SFoffa,GLosurdo,MMaggiore,GMatoneandRSturani179 12 GeneralitiesonthestochasticGWbackground 181 12.1 Introduction 181 12.2 Definitions 184 12.2.1 (cid:1) (f)andtheoptimalSNR 184 gw 12.2.2 Thecharacteristicamplitude 187 12.2.3 Thecharacteristicnoiselevel 189 12.3 Theoverlapreductionfunction 191 12.3.1 Twointerferometers 193 12.3.2 Interferometer—bar 196 12.3.3 Interferometer—sphere 196 12.4 AchievablesensitivitiestotheSGWB 197 12.4.1 Singledetectors 197 12.4.2 Twodetectors 199 12.4.3 Morethantwodetectors 204 12.5 Observationalbounds 207 13 SourcesofSGWB 211 13.1 Topologicaldefects 211 13.1.1 Strings 214 13.1.2 Hybriddefects 221 13.2 Inflation 223 13.2.1 Classicalpicture 224 13.2.2 Calculationofthespectrum 225 13.3 Stringcosmology 229 13.3.1 Themodel 230 13.3.2 Observationalboundstothespectrum 234 13.4 First-orderphasetransitions 235 13.5 Astrophysicalsources 237 References 239 Contents ix PART4 Theoreticaldevelopments HermannNicolai,AlessandroNagar,DonatoBini,FernandoDeFelice, MaurizioGasperiniandLucBlanchet 243 14 Infinite-dimensionalsymmetriesingravity 245 14.1 Einsteintheory 245 14.1.1 Introduction 245 14.1.2 Mathematicalconventions 245 14.1.3 TheEinstein–Hilbertaction 247 14.1.4 DimensionalreductionD =4→ D =3 247 14.1.5 DimensionalreductionD =3→ D =2 248 14.2 Nonlinearσ-models 252 14.2.1 EhlersLagrangianasanonlinearσ-model 254 14.2.2 TheErnstequation 255 14.2.3 TheMatzner–MisnerLagrangianasanonlinearσ-model 255 14.3 Symmetriesofnonlinearσ-models 257 14.3.1 NonlinearrealizationofSL(2,RRR) 257 E 14.3.2 NonlinearrealizationofSL(2,RRR) 258 MM 14.4 TheGerochgroup 259 14.4.1 ActionofSL(2,RRR) onλ˜, B 259 E 2 14.4.2 ActionofSL(2,RRR) onλ, B 260 MM 14.4.3 TheaffineKac–MoodySL(2,RRR)algebra 260 14.5 Thelinearsystem 261 14.5.1 SolvingEinstein’sequations 261 14.5.2 Thelinearsystem 263 14.5.3 Derivationofthecollidingplanemetricbyfactorization 265 Acknowledgments 267 Furtherreading 267 15 Gyroscopesandgravitationalwaves 268 15.1 Introduction 268 15.2 Splittingformalismandtestparticlemotion:ashortreview 269 15.3 Thespacetimemetric 272 15.4 Searchingforanoperationalframe 274 15.5 Precessionofagyroscopeingeodesicmotion 276 15.6 Conclusions 278 References 278 16 Elementaryintroduction to pre-bigbang cosmologyand to the relic gravitonbackground 280 16.1 Introduction 280 16.2 Motivations:dualitysymmetry 283 16.3 Kinematics:shrinkinghorizons 289 16.4 Openproblemsandphenomenologicalconsequences 294 x Contents 16.5 Cosmologicalperturbationtheory 297 16.5.1 Choiceoftheframe 297 16.5.2 Choiceofthegauge 299 16.5.3 Normalizationoftheamplitude 302 16.5.4 Computationofthespectrum 304 16.6 Therelicgravitonbackground 309 16.7 Conclusion 316 Acknowledgments 316 AppendixA.Thestringeffectiveaction 317 AppendixB.Dualitysymmetry 322 AppendixC.Thestringcosmologyequations 328 References 333 17 Post-Newtoniancomputationofbinaryinspiralwaveforms 338 17.1 Introduction 338 17.2 Summaryofoptimalsignalfiltering 340 17.3 Newtonianbinarypolarizationwaveforms 343 17.4 Newtonianorbitalphaseevolution 346 17.5 Post-Newtonianwavegeneration 349 17.5.1 Fieldequations 349 17.5.2 Sourcemoments 350 17.5.3 Radiativemoments 352 17.6 Inspiralbinarywaveform 354 References 356 PART5 Numericalrelativity EdwardSeidel 359 18 Numericalrelativity 361 18.1 Overview 361 18.2 Einsteinequationsforrelativity 363 18.2.1 Constraintequations 365 18.2.2 Evolutionequations 367 18.3 Stillnewerformulations:towardsastableevolutionsystem 369 18.3.1 Generalrelativistichydrodynamics 376 18.3.2 Boundaryconditions 378 18.3.3 Specialdifficultieswithblackholes 379 18.4 Toolsforanalysingthenumericalspacetimes 382 18.4.1 Horizonfinders 382 18.4.2 Locatingtheapparenthorizons 383 18.4.3 Locatingtheeventhorizons 385 18.4.4 Waveextraction 386 18.5 Computationalscience,numericalrelativity,andthe‘Cactus’code 388

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