(ed.). Gravitational waves (IOP, 2001)(422s).

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xContents16.5 Cosmological perturbation theory 29716.5.1 Choice of the frame 29716.5.2 Choice of the gauge 29916.5.3 Normalization of the amplitude 30216.5.4 Computation of the spectrum 30416.6 The relic graviton background 30916.7 Conclusion 316Acknowledgments 316Appendix A. The string effective action 317Appendix B. Duality symmetry 322Appendix C. The string cosmology equations 328References 33317 Post-Newtonian computation of binary inspiral waveforms 33817.1 Introduction 33817.2 Summary of optimal signal filtering 34017.3 Newtonian binary polarization waveforms 34317.4 Newtonian orbital phase evolution 34617.5 Post-Newtonian wave generation 34917.5.1 Field equations 34917.5.2 Source moments 35017.5.3 Radiative moments 35217.6 Inspiral binary waveform 354References 356PART 5Numerical relativityEdward Seidel 35918 Numerical relativity 36118.1 Overview 36118.2 Einstein equations for relativity 36318.2.1 Constraint equations 36518.2.2 Evolution equations 36718.3 Still newer formulations: towards a stable evolution system 36918.3.1 General relativistic hydrodynamics 37618.3.2 Boundary conditions 37818.3.3 Special difficulties with black holes 37918.4 Tools for analysing the numerical spacetimes 38218.4.1 Horizon finders 38218.4.2 Locating the apparent horizons 38318.4.3 Locating the event horizons 38518.4.4 Wave extraction 38618.5 Computational science, numerical relativity, and the ‘Cactus’ code 388
Contentsxi18.5.1 The computational challenges of numerical relativity 38818.6 Cactus computational toolkit 38918.6.1 Adaptive mesh refinement 39118.7 Recent applications and progress 39218.7.1 Evolving pure gravitational waves 39218.7.2 Black holes 39418.8 Summary 399Acknowledgments 40018.9 Further reading 40018.9.1 Overviews/formalisms of numerical relativity 40018.9.2 Numerical techniques 40118.9.3 Gauge conditions 40118.9.4 Black hole initial data 40118.9.5 Black hole evolution 40118.9.6 Black hole excision 40218.9.7 Perturbation theory and waveform extraction 40218.9.8 Event and apparent horizons 40218.9.9 Pure gravitational waves 40318.9.10 Numerical codes 403References 403Index 409
Page 1: GRAVITATIONAL WAVES
Page 4 and 5: c IOP Publishing Ltd 2001All righ
Page 6 and 7: viContents4 Astrophysics of gravita
Page 8 and 9: viiiContents11.3 Gravitational wave
Page 13 and 14: PrefaceGravitational waves today re
Page 15 and 16: 2 Gravitational waves, theory and e
Page 23 and 24: 10 Gravitational waves, theory and
Page 26 and 27: SynopsisGravitational waves and the
Page 28 and 29: Chapter 2Elements of gravitational
Page 30 and 31: Using the TT gauge to understand gr
Page 32 and 33: Interaction of gravitational waves
Page 34 and 35: Analysis of beam detectors 21This d
Page 36 and 37: Exercises for chapter 2 232. Show t
Page 38 and 39: Gravitational-wave detectors 25indi
Page 40 and 41: Gravitational-wave observables 27th
Page 42 and 43: The physics of interferometers 29
Page 44 and 45: The physics of interferometers 31Dr
Page 46 and 47: The physics of interferometers 33Fi
Page 48 and 49: The physics of resonant mass detect
Page 50 and 51: The physics of resonant mass detect
Page 52 and 53: A detector in space 39LISA has been
Page 54 and 55: Gravitational and electromagnetic w
Page 56 and 57: Chapter 4Astrophysics of gravitatio
Page 58 and 59: Sources detectable from ground and
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Sources detectable from ground and
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Sources detectable from ground and
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Variational principles and the ener
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Variational principles and the ener
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Practical applications of the Isaac
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Exercises for chapter 5 57(f)This s
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Expansion for the far field of a sl
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Application of the TT gauge to the
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6.4.1 Mass-quadrupole radiationEner
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Chapter 7Source calculationsNow tha
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The r-modes 73As we mentioned in ch
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The r-modes 75instability. In an id
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The r-modes 77Table 7.1. Gravitatio
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The r-modes 79evolution turns out t
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ReferencesWe have divided the refer
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References 83[19] van der Klis M 19
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Solutions to exercises 85For this p
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Solutions to exercises 87The gauge
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Chapter 8Resonant detectors for gra
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Sensitivity and bandwidth of resona
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8.2 Sensitivity for various GW sign
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Sensitivity for various GW signals
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Recent results obtained with the re
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Discussion and conclusions 101Figur
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Chapter 9The Earth-based large inte
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Introduction 105Figure 9.1. The sim
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h(sqrt(1/Hz))10 −610 −810 −10
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18.5 cmThe SA suspension and requir
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A few words about the Low Frequency
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Conclusion 113Figure 9.7. The R and
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Chapter 10LISA: A proposed joint ES
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Description of the LISA mission 117
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Expected gravitational-wave results
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References 149[8] Folkner W M 1998
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References 151[68] Miralda-Escuda J
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Introduction 153detect GWs with a s
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Testing theories of gravity 155•
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0Testing theories of gravity 157the
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Taking the scalar product we findGr
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Gravitational wave radiation in the
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The hollow sphere 169and introduced
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Scalar-tensor cross sections 171mon
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Scalar-tensor cross sections 173Tab
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Scalar-tensor cross sections 175Tab
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References 177Frossati G and Coccia
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Chapter 12Generalities on the stoch
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Introduction 183contribution to the
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Definitions 185The value of H 0 is
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Definitions 18712.2.2 The character
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Definitions 189or, dividing by the
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The overlap reduction function 191O
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The overlap reduction function 193T
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The overlap reduction function 195F
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Achievable sensitivities to the SGW
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Observational bounds 207Table 12.10
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equation gives immediately(ρgwρ
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Chapter 13Sources of SGWBHere we re
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Topological defects 213This correla
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Topological defects 215It can be sh
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Topological defects 217(i)A loop ra
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Topological defects 219• A peak n
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Topological defects 22113.1.2 Hybri
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Inflation 223Hubble radius and when
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Inflation 225as a first approximati
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Inflation 227the lower bound to the
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String cosmology 22913.3 String cos
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String cosmology 231HPre-big bangPo
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String cosmology 233Figure 13.6. h
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First-order phase transitions 23580
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Astrophysical sources 237which is t
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References 239of [71]). However, fo
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References 241[39] Liddle A R 2000
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PART 4THEORETICAL DEVELOPMENTSHerma
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246 Infinite-dimensional symmetries
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Chapter 15Gyroscopes and gravitatio
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270 Gyroscopes and gravitational wa
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Chapter 16Elementary introduction t
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282 Elementary introduction to pre-
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Chapter 17Post-Newtonian computatio
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340 Post-Newtonian computation of b
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PART 5NUMERICAL RELATIVITYEdward Se
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362 Numerical relativityspite of mo
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364 Numerical relativityterms, of m
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366 Numerical relativityHere we hav
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368 Numerical relativityinformation
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370 Numerical relativityThe Palma,
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372 Numerical relativityHyperbolic
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374 Numerical relativityEinstein di
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376 Numerical relativityare the abi
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378 Numerical relativityeach cell i
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380 Numerical relativityFigure 18.1
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382 Numerical relativity1D code [45
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384 Numerical relativityfunctions,
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386 Numerical relativityto a very a
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388 Numerical relativity18.5 Comput
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390 Numerical relativitynumerics an
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392 Numerical relativityinitial dis
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396 Numerical relativityof these re
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400 Numerical relativityof Einstein
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402 Numerical relativity18.9.5.2 Co
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404 Numerical relativity[23] Ashby
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406 Numerical relativity[101] Shapi
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408 Numerical relativity(Singapore:
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410 IndexEhlers Lagrangian, 254Eins
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412 Indexscalarspherical harmonics,
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