410 IndexEhlers Lagrangian, 254Einstein equations, 245including matter, 51lineariz<strong>ed</strong> theory, 16vacuum, 51elasticity equation, 169Ernst equation, 255, 262EXPLORER, 99, 197Fermi–Walker transport, 8fieldgravitomagnetic, 3axion, 250current-quadrupole, 60, 65, 66dilaton, 7, 250duality symmetry, 284mass-octupole, 60, 65mass-quadrupole, 60, 62, 72scalar, 153forc<strong>ed</strong>riving, 156tidal, 18frameJordan–Fierz, 160local free-falling, 153frequencybandwidth, 5monopole resonant, 159gamma-ray bursts, 45, 46gaugecondition, 161, 247conformal, 7, 249Lorentz–Hilbert, 16preserving choice, 253transformation, 16, 52transverse-traceless, 4triangular, 254TT, 17gauge conditionsin relativity, 373GEO 600, 26, 33, 195geodesic equation, 18geon, 3Geroch group, 7, 259gravitationalantenna, 315collapse, 43, 165, 171, 173geon, 3radiation, 15self-energy, 163stress-energy tensor, 54gravitational wave, 15action, 52burst, 27, 32, 37energy, 55continuous, 27cosmological relic, 7in lineariz<strong>ed</strong> theory, 15in short-wave approximation, 52Jordan–Brans–Dicke, 169, 171observable, 26polarization states, 159scalar, 6, 152, 159stochastic, 7graviton spectrum, 304, 308groupsymmetry, 7gyroscope, 8, 268, 271, 273, 276precession, 271, 276Helmholtz equation, 162horizons, 292event, 386Hubble constant, 56, 73inflation, 223, 289interferometer, 22, 25, 28, 104Fabry–Perot, 28gravity gradient noise, 31Michelson, 28shot noise, 30, 105thermal noise, 30, 106uncertainty principle noise, 31vibrational noise, 31Isaacson tensor, 54JGWO, 26
Index 411Kaluza–Klein, 7, 153, 247, 251Killing vector, 7, 245, 247Kramer–Neugebauertransformation, 256LagrangianEhlers, 7Einstein–Hilbert, 7Matzner–Misner, 7Lamé coefficients, 154Lie group, 252LIGO, 5, 26, 34, 184LISA, 5, 26, 38, 115, 185antenna, 116loop corrections, 304masstest, 5Matzner–Misner Lagrangian, 252,255metricFerrari–Ibanez, 266Minkowski, 16trace-revers<strong>ed</strong> perturbation, 16minisuperspace, 295modesmonopole, 159, 169normal, 155, 168quadrupole, 169Rossby, 75scalar, 168spheroidal, 155, 157toroidal, 155, 156vibrational, 158Multiple moments, 339, 350–352NAUTILUS, 38, 99, 197neutron star, 45, 46, 79accreting, 46Newman–Penrose parameter, 158NIOBE, 99noiseground, 6narrowband, 167photon shot, 5seismic, 5, 6wideband, 167nonlinear σ -model, 7, 252nucleosynthesis, 310O(d, d) symmetry, 327optical theorem, 170Optimal signal filtering, 340, 341,344, 354perturbationof background metric, 16, 50velocity, 75phase transitions, 235photodetector, 5polarizationcircular, 18collinear, 8non-collinear, 8tensor, 17, 26Post-Newtonianapproximation, 339, 346expansion, 339, 347, 350, 351power recycling, 30pre-big bang, string cosmology, 281primordial magnetic fields, 296pulsar, 47timing, 22pulsars, 46quality factor, 4, 155r-modes, 4, 43, 46, 73, 75damping time, 76linear evolution, 76nonlinear evolution, 77radiationcurrent-quadrupole, 4, 75mass-quadrupole, 4, 69ranging to spaceraft, 21relic axions, 296relic gravitons, 295retard<strong>ed</strong> integral, 58
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GRAVITATIONAL WAVES
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c IOP Publishing Ltd 2001All righ
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viContents4 Astrophysics of gravita
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viiiContents11.3 Gravitational wave
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xContents16.5 Cosmological perturba
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PrefaceGravitational waves today re
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2 Gravitational waves, theory and e
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4 Gravitational waves, theory and e
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6 Gravitational waves, theory and e
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8 Gravitational waves, theory and e
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10 Gravitational waves, theory and
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SynopsisGravitational waves and the
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Chapter 2Elements of gravitational
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Using the TT gauge to understand gr
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Interaction of gravitational waves
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Analysis of beam detectors 21This d
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Exercises for chapter 2 232. Show t
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Gravitational-wave detectors 25indi
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Gravitational-wave observables 27th
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The physics of interferometers 29
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The physics of interferometers 31Dr
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The physics of interferometers 33Fi
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The physics of resonant mass detect
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The physics of resonant mass detect
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A detector in space 39LISA has been
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Gravitational and electromagnetic w
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Chapter 4Astrophysics of gravitatio
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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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Application of the TT gauge to the
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Application of the TT gauge to the
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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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Description of the LISA mission 119
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Description of the LISA mission 121
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Description of the LISA mission 123
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Description of the LISA mission 125
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Description of the LISA mission 127
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Description of the LISA mission 129
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Description of the LISA mission 131
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Expected gravitational-wave results
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Expected gravitational-wave results
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Expected gravitational-wave results
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Expected gravitational-wave results
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Expected gravitational-wave results
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Expected gravitational-wave results
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Expected gravitational-wave results
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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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Gravitational wave radiation in the
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Gravitational wave radiation in the
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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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Achievable sensitivities to the SGW
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Achievable sensitivities to the SGW
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Achievable sensitivities to the SGW
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Achievable sensitivities to the SGW
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Observational bounds 207Table 12.10
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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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248 Infinite-dimensional symmetries
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250 Infinite-dimensional symmetries
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252 Infinite-dimensional symmetries
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254 Infinite-dimensional symmetries
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256 Infinite-dimensional symmetries
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258 Infinite-dimensional symmetries
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260 Infinite-dimensional symmetries
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262 Infinite-dimensional symmetries
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264 Infinite-dimensional symmetries
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266 Infinite-dimensional symmetries
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Chapter 15Gyroscopes and gravitatio
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270 Gyroscopes and gravitational wa
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272 Gyroscopes and gravitational wa
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274 Gyroscopes and gravitational wa
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276 Gyroscopes and gravitational wa
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278 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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284 Elementary introduction to pre-
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288 Elementary introduction to pre-
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316 Elementary introduction to pre-
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320 Elementary introduction to pre-
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322 Elementary introduction to pre-
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324 Elementary introduction to pre-
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330 Elementary introduction to pre-
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332 Elementary introduction to pre-
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334 Elementary introduction to pre-
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336 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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342 Post-Newtonian computation of b
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344 Post-Newtonian computation of b
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346 Post-Newtonian computation of b
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348 Post-Newtonian computation of b
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350 Post-Newtonian computation of b
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352 Post-Newtonian computation of b
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354 Post-Newtonian computation of b
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356 Post-Newtonian computation of b
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