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176 Detection of scalar gravitational wavesAcknowledgmentsWe wish to thank very much the organizers of the school for their kind invitationto present this lecture, and all of my collaborators for sharing their insights on thesubject with me.References[1] Thorne K S 1987 Three Hundred Years of Gravitation ed S W Hawking and W Israel(Cambridge: Cambridge University Press)[2] Coccia E, Pizzella G and Ronga F 1995 Gravitational wave experiments Proc. FirstEdoardo Amaldi Conf. (Frascati, 1994) (Singapore: World Scientific)[3] Astone P et al 1993 Phys. Rev. D 47 362[4] Johnson W W 1995 Proc. First Edoardo Amaldi Conf. (Frascati, 1994) (Singapore:World Scientific)[5] Abramovici A et al 1992 Science 26 325Bradaschia C et al 1990 Nucl. Instrum. Methods A 289 518[6] Bianchi M, Coccia E, Colacino C N, Fafone V and Fucito F 1996 Class. QuantumGrav. 13 2865Bianchi M, Brunetti M, Coccia E, Fucito F and Lobo J A 1998 Phys. Rev. D 57 4525Brunetti M, Coccia E, Fafone V and Fucito F 1999 Phys. Rev. D 59 044027Coccia E, Fucito F, Lobo J A and Salvino M 2000 Phys. Rev. D 62 044019[7] Will C M 1993 Theory and Experiment in Gravitational Physics (Cambridge:Cambridge University Press)[8] Jaerish P 1880 J.f. Math. (Crelle) 88Lamb H 1882 Proc. London Mathematical Society vol 13Love A E H 1927 A Treatise on the Mathematical Theory of Elasticity (London:Cambridge University Press)[9] Lobo J A 1995 Phys. Rev. D 52 591[10] Ashby N and Dreitlein J 1975 Phys. Rev. D 12 336[11] Jackson J D 1975 Classical Electrodynamics (New York: Wiley)[12] Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (New York: Freeman)[13] Wagoner R V and Paik H J 1977 Experimental gravitation Proc. Int. Symp. held inPavia 1976 (Roma: Acc. Naz. dei Lincei)[14] Dhurandhar S V and Tinto M 1989 Proc. V Marcel Grossmann Meeting ed D G Blair,M J Buckingham and R Ruffini (Singapore: World Scientific)[15] Zhou C Z and Michelson P F 1995 Phys. Rev. D 51 2517[16] Johnson W W and Merkovitz S M 1993 Phys. Rev. Lett. 70 2367[17] Jordan P 1959 Z. Phys. 157 112Brans C and Dicke R H 1961 Phys. Rev. 124 925[18] Miller J, Schneider M, Soffel M and Ruder H 1991 Astrophys. J. Lett. 382 L101[19] Lee D L 1974 Phys. Rev. D 10 2374[20] Dewey D 1987 Phys. Rev. D 36 1577[21] Coccia E and Fafone V 1996 Phys. Lett. A 213 16[22] Astone P, Pallottino G V and Pizzella G 1997 Class. Quantum Grav. 14 2019[23] Clark J P A and Eardley D M 1977 Astrophys. J. 215 311[24] Frossati G and Coccia E 1994 Cryogenics 34 (ICEC Supplement) 9
References 177Frossati G and Coccia E 1994 Cryogenics 34 (ICEC Supplement) 304[25] Coccia E, Fafone V, Frossati G, Lobo J A and Ortega J A 1998 Phys. Rev. D 57 2051[26] Weinberg S 1972 Gravitation and Cosmology (New York: Wiley)[27] Shibata M, Nakao K and Nakamura T 1994 Phys. Rev. D 50 7304Saijo M, Shinkai H and Maeda K 1997 Phys. Rev. D 56 785
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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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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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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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Page 137 and 138: Description of the LISA mission 125
Page 145 and 146: Expected gravitational-wave results
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Page 163 and 164: References 151[68] Miralda-Escuda J
Page 165 and 166: Introduction 153detect GWs with a s
Page 167 and 168: Testing theories of gravity 155•
Page 169 and 170: 0Testing theories of gravity 157the
Page 171 and 172: Taking the scalar product we findGr
Page 173 and 174: Gravitational wave radiation in the
Page 181 and 182: The hollow sphere 169and introduced
Page 183 and 184: Scalar-tensor cross sections 171mon
Page 185 and 186: Scalar-tensor cross sections 173Tab
Page 187: Scalar-tensor cross sections 175Tab
Page 192 and 193: Chapter 12Generalities on the stoch
Page 194 and 195: Introduction 183contribution to the
Page 196 and 197: Definitions 185The value of H 0 is
Page 198 and 199: Definitions 18712.2.2 The character
Page 200 and 201: Definitions 189or, dividing by the
Page 202 and 203: The overlap reduction function 191O
Page 204 and 205: The overlap reduction function 193T
Page 206 and 207: The overlap reduction function 195F
Page 208 and 209: Achievable sensitivities to the SGW
Page 218 and 219: Observational bounds 207Table 12.10
Page 220 and 221: equation gives immediately(ρgwρ
Page 222 and 223: Chapter 13Sources of SGWBHere we re
Page 224 and 225: Topological defects 213This correla
Page 226 and 227: Topological defects 215It can be sh
Page 228 and 229: Topological defects 217(i)A loop ra
Page 230 and 231: Topological defects 219• A peak n
Page 232 and 233: Topological defects 22113.1.2 Hybri
Page 234 and 235: Inflation 223Hubble radius and when
Page 236 and 237: 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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