This most up-to-date, one-stop reference combines coverage of both theory and observational techniques, with introductory sections to bring all readers up to the same level. Written by outstanding researchers directly involved with the scientific program of the Laser Interferometer Gravitational-Wave Observatory (LIGO), the book begins with a brief review of general relativity before going on to describe the physics of gravitational waves and the astrophysical sources of gravitational radiation. Further sections cover gravitational wave detectors, data analysis, and the outlook of gravitational wave astronomy and astrophysics.
Table of Contents:
Preface xi
List of Examples xiii
Introduction 1
References 2
1 Prologue 3
1.1 Tides in Newton’s Gravity 3
1.2 Relativity 8
2 A Brief Review of General Relativity 11
2.1 Differential Geometry 12
2.1.1 Coordinates and Distances 12
2.1.2 Vectors 14
2.1.3 Connections 16
2.1.4 Geodesics 24
2.1.5 Curvature 25
2.1.6 Geodesic Deviation 31
2.1.7 Ricci and Einstein Tensors 32
2.2 Slow Motion in Weak Gravitational Fields 32
2.3 Stress-Energy Tensor 34
2.3.1 Perfect Fluid 36
2.3.2 Electromagnetism 38
2.4 Einstein’s Field Equations 38
2.5 Newtonian Limit of General Relativity 40
2.5.1 Linearized Gravity 40
2.5.2 Newtonian Limit 43
2.5.3 Fast Motion 44
2.6 Problems 45
References 47
3 Gravitational Waves 49
3.1 Description of Gravitational Waves 49
3.1.1 Propagation of Gravitational Waves 55
3.2 Physical Properties of Gravitational Waves 58
3.2.1 Effects of Gravitational Waves 58
3.2.2 Energy Carried by a Gravitational Wave 66
3.3 Production of Gravitational Radiation 69
3.3.1 Far- and Near-Zone Solutions 69
3.3.2 Gravitational Radiation Luminosity 74
3.3.3 Radiation Reaction 78
3.3.4 Angular Momentum Carried by Gravitational Radiation 80
3.4 Demonstration: Rotating Triaxial Ellipsoid 80
3.5 Demonstration: Orbiting Binary System 84
3.6 Problems 91
References 95
4 Beyond the Newtonian Limit 97
4.1 Post-Newtonian 97
4.1.1 System of Point Particles 104
4.1.2 Two-Body Post-Newtonian Motion 109
4.1.3 Higher-Order Post-Newtonian Waveforms for Binary Inspiral 114
4.2 Perturbation about Curved Backgrounds 114
4.2.1 Gravitational Waves in Cosmological Spacetimes 119
4.2.2 Black Hole Perturbation 123
4.3 Numerical Relativity 130
4.3.1 The Arnowitt–Deser–Misner (ADM) Formalism 130
4.3.2 Coordinate Choice 139
4.3.3 Initial Data 141
4.3.4 Gravitational-Wave Extraction 143
4.3.5 Matter 143
4.3.6 Numerical Methods 144
4.4 Problems 145
References 147
5 Sources of Gravitational Radiation 149
5.1 Sources of Continuous Gravitational Waves 151
5.2 Sources of Gravitational-Wave Bursts 157
5.2.1 Coalescing Binaries 157
5.2.2 Gravitational Collapse 165
5.2.3 Bursts from Cosmic String Cusps 169
5.2.4 Other Burst Sources 170
5.3 Sources of a Stochastic Gravitational-Wave Background 171
5.3.1 Cosmological Backgrounds 172
5.3.2 Astrophysical Backgrounds 191
5.4 Problems 194
References 196
6 Gravitational-Wave Detectors 197
6.1 Ground-Based Laser Interferometer Detectors 198
6.1.1 Notes on Optics 203
6.1.2 Fabry–Pérot Cavity 207
6.1.3 Michelson Interferometer 211
6.1.4 Power Recycling 214
6.1.5 Readout 216
6.1.6 Frequency Response of the Initial LIGO Detector 221
6.1.7 Sensor Noise 226
6.1.8 Environmental Sources of Noise 230
6.1.9 Control System 239
6.1.10 Gravitational-Wave Response of an Interferometric Detector 241
6.1.11 Second Generation Ground-Based Interferometers (and Beyond) 244
6.2 Space-Based Detectors 251
6.2.1 Spacecraft Tracking 251
6.2.2 Lisa 252
6.2.3 Decihertz Experiments 256
6.3 Pulsar Timing Experiments 256
6.4 Resonant Mass Detectors 260
6.5 Problems 265
References 267
7 Gravitational-Wave Data Analysis 269
7.1 Random Processes 269
7.1.1 Power Spectrum 270
7.1.2 Gaussian Noise 273
7.2 Optimal Detection Statistic 275
7.2.1 Bayes’s Theorem 275
7.2.2 Matched Filter 276
7.2.3 Unknown Matched Filter Parameters 277
7.2.4 Statistical Properties of the Matched Filter 279
7.2.5 Matched Filter with Unknown Arrival Time 281
7.2.6 Template Banks of Matched Filters 282
7.3 Parameter Estimation 286
7.3.1 Measurement Accuracy 286
7.3.2 Systematic Errors in Parameter Estimation 289
7.3.3 Confidence Intervals 291
7.4 Detection Statistics for Poorly Modelled Signals 293
7.4.1 Excess-Power Method 293
7.5 Detection in Non-Gaussian Noise 295
7.6 Networks of Gravitational-Wave Detectors 298
7.6.1 Co-located and Co-aligned Detectors 298
7.6.2 General Detector Networks 300
7.6.3 Time-Frequency Excess-Power Method for a Network of Detectors 303
7.6.4 Sky Position Localization for Gravitational-Wave Bursts 305
7.7 Data Analysis Methods for Continuous-Wave Sources 307
7.7.1 Search for Gravitational Waves from a Known, Isolated Pulsar 309
7.7.2 All-Sky Searches for Gravitational Waves from Unknown Pulsars 316
7.8 Data Analysis Methods for Gravitational-Wave Bursts 317
7.8.1 Searches for Coalescing Compact Binary Sources 318
7.8.2 Searches for Poorly Modelled Burst Sources 332
7.9 Data Analysis Methods for Stochastic Sources 333
7.9.1 Stochastic Gravitational-Wave Point Sources 344
7.10 Problems 345
References 347
8 Epilogue: Gravitational-Wave Astronomy and Astrophysics 349
8.1 Fundamental Physics 349
8.2 Astrophysics 351
References 353
Appendix A Gravitational-Wave Detector Data 355
A.1 Gravitational-Wave Detector Site Data 355
A.2 Idealized Initial LIGO Model 359
References 361
Appendix B Post-Newtonian Binary Inspiral Waveform 363
B.1 TaylorT1 Orbital Evolution 366
B.2 TaylorT2 Orbital Evolution 366
B.3 TaylorT3 Orbital Evolution 367
B.4 TaylorT4 Orbital Evolution 368
B.5 TaylorF2 Stationary Phase 369
References 370
Index 371
About the Author :
Jolien D. E. Creighton is an Associate Professor of Physics at the University of Wisconsin?Milwaukee and a member of the LIGO Scientific Collaboration, which he joined in 1998. He received his doctoral degree at the University of Waterloo where he studied the thermodynamical properties of black holes.
Warren G. Anderson is a scientist at the University of Wisconsin?Milwaukee and a member of the LIGO Scientific Collaboration, which he joined in 1998. He received his doctorate at the University of Alberta under Werner Israel, where he worked on Black Hole physics, and has also held a tenure track position at The University of Texas at Brownsville. He also received Master's degrees in Medical Physics (University of Alberta) and Applied Mathematics (University of Waterloo).
