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References 9in especially simple cases. Thus, to find solutions of the Einstein’s equations,for example in a system with emission of gravitational radiation, we need to findnumerical solutions of these field equations, i.e. we need numerical relativity.Nevertheless, even the numerical approach to the emission of gravitational wavesin strong field is extremely difficult and computer-time consuming. For example,as Seidel explains, the computer simulation of the coalescence of a compact objectbinary will require several years of super-computer time. However, special codesto solve the complete set of Einstein’s equations have been designed that run veryefficiently on large-scale parallel computers, in particular, one of these codes, theCactus Computational Toolkit is presented in this paper. Then, after a descriptionof the numerical formulation of the theory of general relativity, constraintequations and evolution equations, the numerical techniques for solving theevolution equations are reported and finally some recent applications, includinggravitational waves and the evolution and collisions of black holes, are presented.It is important to note that there have been and there are large collaborations innumerical relativity, including: the NSF Black Hole Grand Challenge Project, theNASA Neutron Star Grand Challenge Project, the NCSA/Potsdam/WashingtonUniversity numerical relativity collaboration and a EU European collaboration often institutions.References[1] Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (New York: Freeman)[2] Ciufolini I and Wheeler J A 1995 Gravitation and Inertia (Princeton, NJ: PrincetonUniversity Press)[3] Thorne K S 1987 Three Hundred Years of Gravitation ed S W Hawking and W Israel(Cambridge: Cambridge University Press)[4] Einstein A 1916 Preuss. Akad. Wiss. Berlin, Sitzber. 688[5] Grishchuk L P and Polnarev A G 1980 General Relativity and Gravitation, OneHundred Years After the Birth of Albert Einstein ed A Held (New York: Plenum)[6] Douglass D H and Braginsky V B 1979 General Relativity, An Einstein CentenarySurvey ed S W Hawking and W Israel (Cambridge: Cambridge University Press)[7] Landau L D and Lifshitz E M 1962 The Classical Theory of Fields (Reading, MA:Addison-Wesley)[8] Bondi H 1957 Nature 179 1072See also Bondi H and McCrea W H 1960 Proc. Camb. Phil. Soc. 56 410[9] Wheeler J A 1955 Phys. Rev. 97 511[10] Weber J 1961 General Relativity and Gravitational Waves (New York: Wiley–Interscience)[11] Weinberg S 1972 Gravitation and Cosmology (New York: Wiley)[12] Hulse R A and Taylor J H 1975 Astrophys. J. 195 L51
10 Gravitational waves, theory and experiment (an overview)[13] Ciufolini I et al 1996 Nuovo Cimento A 109 575See also Ciufolini I et al 1997 Class. Quantum Grav. 14 2701Ciufolini I et al 1998 Science 279 2100[14] Will C M 1993 Theory and Experiment in Gravitational Physics (Cambridge:Cambridge University Press)
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 10 and 11: xContents16.5 Cosmological perturba
Page 13 and 14: PrefaceGravitational waves today re
Page 15 and 16: 2 Gravitational waves, theory and e
Page 21: 8 Gravitational waves, theory and e
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
Page 64 and 65: Variational principles and the ener
Page 66 and 67: Variational principles and the ener
Page 68 and 69: Practical applications of the Isaac
Page 70 and 71: 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:
Page 420 and 421:
410 IndexEhlers Lagrangian, 254Eins
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412 Indexscalarspherical harmonics,
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