Gravitational-Wave Physics and Astronomy -- Contents -- Preface -- List of Examples -- Introduction -- References -- 1 Prologue -- 1.1 Tides in Newton's Gravity -- 1.2 Relativity -- 2 A Brief Review of General Relativity -- 2.1 Differential Geometry -- 2.1.1 Coordinates and Distances -- 2.1.2 Vectors -- 2.1.3 Connections -- 2.1.4 Geodesics -- 2.1.5 Curvature -- 2.1.6 Geodesic Deviation -- 2.1.7 Ricci and Einstein Tensors -- 2.2 Slow Motion in Weak Gravitational Fields -- 2.3 Stress-Energy Tensor -- 2.3.1 Perfect Fluid -- 2.3.2 Electromagnetism -- 2.4 Einstein's Field Equations -- 2.5 Newtonian Limit of General Relativity -- 2.5.1 Linearized Gravity -- 2.5.2 Newtonian Limit -- 2.5.3 Fast Motion -- 2.6 Problems -- References -- 3 Gravitational Waves -- 3.1 Description of Gravitational Waves -- 3.1.1 Propagation of Gravitational Waves -- 3.2 Physical Properties of Gravitational Waves -- 3.2.1 Effects of Gravitational Waves -- 3.2.2 Energy Carried by a Gravitational Wave -- 3.3 Production of Gravitational Radiation -- 3.3.1 Far- and Near-Zone Solutions -- 3.3.2 Gravitational Radiation Luminosity -- 3.3.3 Radiation Reaction -- 3.3.4 Angular Momentum Carried by Gravitational Radiation -- 3.4 Demonstration: Rotating Triaxial Ellipsoid -- 3.5 Demonstration: Orbiting Binary System -- 3.6 Problems -- References -- 4 Beyond the Newtonian Limit -- 4.1 Post-Newtonian -- 4.1.1 System of Point Particles -- 4.1.2 Two-Body Post-Newtonian Motion -- 4.1.3 Higher-Order Post-Newtonian Waveforms for Binary Inspiral -- 4.2 Perturbation about Curved Backgrounds -- 4.2.1 Gravitational Waves in Cosmological Spacetimes -- 4.2.2 Black Hole Perturbation -- 4.3 Numerical Relativity -- 4.3.1 The Arnowitt-Deser-Misner (ADM) Formalism -- 4.3.2 Coordinate Choice -- 4.3.3 Initial Data -- 4.3.4 Gravitational-Wave Extraction -- 4.3.5 Matter -- 4.3.6 Numerical Methods -- 4.4 Problems.

References -- 5 Sources of Gravitational Radiation -- 5.1 Sources of Continuous Gravitational Waves -- 5.2 Sources of Gravitational-Wave Bursts -- 5.2.1 Coalescing Binaries -- 5.2.2 Gravitational Collapse -- 5.2.3 Bursts from Cosmic String Cusps -- 5.2.4 Other Burst Sources -- 5.3 Sources of a Stochastic Gravitational-Wave Background -- 5.3.1 Cosmological Backgrounds -- 5.3.2 Astrophysical Backgrounds -- 5.4 Problems -- References -- 6 Gravitational-Wave Detectors -- 6.1 Ground-Based Laser Interferometer Detectors -- 6.1.1 Notes on Optics -- 6.1.2 Fabry-Pérot Cavity -- 6.1.3 Michelson Interferometer -- 6.1.4 Power Recycling -- 6.1.5 Readout -- 6.1.6 Frequency Response of the Initial LIGO Detector -- 6.1.7 Sensor Noise -- 6.1.8 Environmental Sources of Noise -- 6.1.9 Control System -- 6.1.10 Gravitational-Wave Response of an Interferometric Detector -- 6.1.11 Second Generation Ground-Based Interferometers (and Beyond) -- 6.2 Space-Based Detectors -- 6.2.1 Spacecraft Tracking -- 6.2.2 LISA -- 6.2.3 Decihertz Experiments -- 6.3 Pulsar Timing Experiments -- 6.4 Resonant Mass Detectors -- 6.5 Problems -- References -- 7 Gravitational-Wave Data Analysis -- 7.1 Random Processes -- 7.1.1 Power Spectrum -- 7.1.2 Gaussian Noise -- 7.2 Optimal Detection Statistic -- 7.2.1 Bayes's Theorem -- 7.2.2 Matched Filter -- 7.2.3 Unknown Matched Filter Parameters -- 7.2.4 Statistical Properties of the Matched Filter -- 7.2.5 Matched Filter with Unknown Arrival Time -- 7.2.6 Template Banks of Matched Filters -- 7.3 Parameter Estimation -- 7.3.1 Measurement Accuracy -- 7.3.2 Systematic Errors in Parameter Estimation -- 7.3.3 Confidence Intervals -- 7.4 Detection Statistics for Poorly Modelled Signals -- 7.4.1 Excess-Power Method -- 7.5 Detection in Non-Gaussian Noise -- 7.6 Networks of Gravitational-Wave Detectors -- 7.6.1 Co-located and Co-aligned Detectors.

7.6.2 General Detector Networks -- 7.6.3 Time-Frequency Excess-Power Method for a Network of Detectors -- 7.6.4 Sky Position Localization for Gravitational-Wave Bursts -- 7.7 Data Analysis Methods for Continuous-Wave Sources -- 7.7.1 Search for Gravitational Waves from a Known, Isolated Pulsar -- 7.7.2 All-Sky Searches for Gravitational Waves from Unknown Pulsars -- 7.8 Data Analysis Methods for Gravitational-Wave Bursts -- 7.8.1 Searches for Coalescing Compact Binary Sources -- 7.8.2 Searches for Poorly Modelled Burst Sources -- 7.9 Data Analysis Methods for Stochastic Sources -- 7.9.1 Stochastic Gravitational-Wave Point Sources -- 7.10 Problems -- References -- 8 Epilogue: Gravitational-Wave Astronomy and Astrophysics -- 8.1 Fundamental Physics -- 8.2 Astrophysics -- References -- Appendix A Gravitational-Wave Detector Data -- A.1 Gravitational-Wave Detector Site Data -- A.2 Idealized Initial LIGO Model -- References -- Appendix B Post-Newtonian Binary Inspiral Waveform -- B.1 TaylorT1 Orbital Evolution -- B.2 TaylorT2 Orbital Evolution -- B.3 TaylorT3 Orbital Evolution -- B.4 TaylorT4 Orbital Evolution -- B.5 TaylorF2 Stationary Phase -- References -- Index.