Gravitational-Wave Physics and Astronomy

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).

• Preface xiList of Examples xiiiIntroduction 1References 21 Prologue 31.1 Tides in Newton’s Gravity 31.2 Relativity 82 A Brief Review of General Relativity 112.1 Differential Geometry 122.1.1 Coordinates and Distances 122.1.2 Vectors 142.1.3 Connections 162.1.4 Geodesics 242.1.5 Curvature 252.1.6 Geodesic Deviation 312.1.7 Ricci and Einstein Tensors 322.2 Slow Motion in Weak Gravitational Fields 322.3 Stress-Energy Tensor 342.3.1 Perfect Fluid 362.3.2 Electromagnetism 382.4 Einstein’s Field Equations 382.5 Newtonian Limit of General Relativity 402.5.1 Linearized Gravity 402.5.2 Newtonian Limit 432.5.3 Fast Motion 442.6 Problems 45References 473 Gravitational Waves 493.1 Description of Gravitational Waves 493.1.1 Propagation of Gravitational Waves 553.2 Physical Properties of Gravitational Waves 583.2.1 Effects of Gravitational Waves 583.2.2 Energy Carried by a Gravitational Wave 663.3 Production of Gravitational Radiation 693.3.1 Far- and Near-Zone Solutions 693.3.2 Gravitational Radiation Luminosity 743.3.3 Radiation Reaction 783.3.4 Angular Momentum Carried by Gravitational Radiation 803.4 Demonstration: Rotating Triaxial Ellipsoid 803.5 Demonstration: Orbiting Binary System 843.6 Problems 91References 954 Beyond the Newtonian Limit 974.1 Post-Newtonian 974.1.1 System of Point Particles 1044.1.2 Two-Body Post-Newtonian Motion 1094.1.3 Higher-Order Post-Newtonian Waveforms for Binary Inspiral 1144.2 Perturbation about Curved Backgrounds 1144.2.1 Gravitational Waves in Cosmological Spacetimes 1194.2.2 Black Hole Perturbation 1234.3 Numerical Relativity 1304.3.1 The Arnowitt–Deser–Misner (ADM) Formalism 1304.3.2 Coordinate Choice 1394.3.3 Initial Data 1414.3.4 Gravitational-Wave Extraction 1434.3.5 Matter 1434.3.6 Numerical Methods 1444.4 Problems 145References 1475 Sources of Gravitational Radiation 1495.1 Sources of Continuous Gravitational Waves 1515.2 Sources of Gravitational-Wave Bursts 1575.2.1 Coalescing Binaries 1575.2.2 Gravitational Collapse 1655.2.3 Bursts from Cosmic String Cusps 1695.2.4 Other Burst Sources 1705.3 Sources of a Stochastic Gravitational-Wave Background 1715.3.1 Cosmological Backgrounds 1725.3.2 Astrophysical Backgrounds 1915.4 Problems 194References 1966 Gravitational-Wave Detectors 1976.1 Ground-Based Laser Interferometer Detectors 1986.1.1 Notes on Optics 2036.1.2 Fabry–Pérot Cavity 2076.1.3 Michelson Interferometer 2116.1.4 Power Recycling 2146.1.5 Readout 2166.1.6 Frequency Response of the Initial LIGO Detector 2216.1.7 Sensor Noise 2266.1.8 Environmental Sources of Noise 2306.1.9 Control System 2396.1.10 Gravitational-Wave Response of an Interferometric Detector 2416.1.11 Second Generation Ground-Based Interferometers (and Beyond) 2446.2 Space-Based Detectors 2516.2.1 Spacecraft Tracking 2516.2.2 Lisa 2526.2.3 Decihertz Experiments 2566.3 Pulsar Timing Experiments 2566.4 Resonant Mass Detectors 2606.5 Problems 265References 2677 Gravitational-Wave Data Analysis 2697.1 Random Processes 2697.1.1 Power Spectrum 2707.1.2 Gaussian Noise 2737.2 Optimal Detection Statistic 2757.2.1 Bayes’s Theorem 2757.2.2 Matched Filter 2767.2.3 Unknown Matched Filter Parameters 2777.2.4 Statistical Properties of the Matched Filter 2797.2.5 Matched Filter with Unknown Arrival Time 2817.2.6 Template Banks of Matched Filters 2827.3 Parameter Estimation 2867.3.1 Measurement Accuracy 2867.3.2 Systematic Errors in Parameter Estimation 2897.3.3 Confidence Intervals 2917.4 Detection Statistics for Poorly Modelled Signals 2937.4.1 Excess-Power Method 2937.5 Detection in Non-Gaussian Noise 2957.6 Networks of Gravitational-Wave Detectors 2987.6.1 Co-located and Co-aligned Detectors 2987.6.2 General Detector Networks 3007.6.3 Time-Frequency Excess-Power Method for a Network of Detectors 3037.6.4 Sky Position Localization for Gravitational-Wave Bursts 3057.7 Data Analysis Methods for Continuous-Wave Sources 3077.7.1 Search for Gravitational Waves from a Known, Isolated Pulsar 3097.7.2 All-Sky Searches for Gravitational Waves from Unknown Pulsars 3167.8 Data Analysis Methods for Gravitational-Wave Bursts 3177.8.1 Searches for Coalescing Compact Binary Sources 3187.8.2 Searches for Poorly Modelled Burst Sources 3327.9 Data Analysis Methods for Stochastic Sources 3337.9.1 Stochastic Gravitational-Wave Point Sources 3447.10 Problems 345References 3478 Epilogue: Gravitational-Wave Astronomy and Astrophysics 3498.1 Fundamental Physics 3498.2 Astrophysics 351References 353Appendix A Gravitational-Wave Detector Data 355A.1 Gravitational-Wave Detector Site Data 355A.2 Idealized Initial LIGO Model 359References 361Appendix B Post-Newtonian Binary Inspiral Waveform 363B.1 TaylorT1 Orbital Evolution 366B.2 TaylorT2 Orbital Evolution 366B.3 TaylorT3 Orbital Evolution 367B.4 TaylorT4 Orbital Evolution 368B.5 TaylorF2 Stationary Phase 369References 370Index 371