CONTENTS PART I FOUNDATIONS 1. vii

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1 CONTENTS List of Boxes xxvii Preface xxxi Acknowledgments xxxix PART I FOUNDATIONS 1 1 Newtonian Physics: Geometric Viewpoint Introduction The Geometric Viewpoint on the Laws of Physics Purposes of This Chapter Overview of This Chapter Foundational Concepts Tensor Algebra without a Coordinate System Particle Kinetics and Lorentz Force in Geometric Language Component Representation of Tensor Algebra Slot-Naming Index Notation Particle Kinetics in Index Notation Orthogonal Transformations of Bases Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl Volumes, Integration, and Integral Conservation Laws Gauss s and Stokes Theorems The Stress Tensor and Momentum Conservation Examples: Electromagnetic Field and Perfect Fluid Conservation of Momentum Geometrized Units and Relativistic Particles for Newtonian Readers Geometrized Units Energy and Momentum of a Moving Particle 34 Bibliographic Note 35 Track Two; see page xxxiv Nonrelativistic(Newtonian)kinetictheory;seepage96 Relativistic theory; see page 96 vii

2 2 Special Relativity: Geometric Viewpoint Overview Foundational Concepts Inertial Frames, Inertial Coordinates, Events, Vectors, and Spacetime Diagrams The Principle of Relativity and Constancy of Light Speed The Interval and Its Invariance Tensor Algebra without a Coordinate System Particle Kinetics and Lorentz Force without a Reference Frame Relativistic Particle Kinetics: World Lines, 4-Velocity, 4-Momentum and Its Conservation, 4-Force Geometric Derivation of the Lorentz Force Law Component Representation of Tensor Algebra Lorentz Coordinates Index Gymnastics Slot-Naming Notation Particle Kinetics in Index Notation and in a Lorentz Frame Lorentz Transformations Spacetime Diagrams for Boosts Time Travel Measurement of Time; Twins Paradox Wormholes Wormhole as Time Machine Directional Derivatives, Gradients, and the Levi-Civita Tensor Nature of Electric and Magnetic Fields; Maxwell s Equations Volumes, Integration, and Conservation Laws Spacetime Volumes and Integration Conservation of Charge in Spacetime Conservation of Particles, Baryon Number, and Rest Mass Stress-Energy Tensor and Conservation of 4-Momentum Stress-Energy Tensor Momentum Conservation Stress-Energy Tensors for Perfect Fluids and Electromagnetic Fields 85 Bibliographic Note 88 PART II STATISTICAL PHYSICS 91 3 Kinetic Theory Overview Phase Space and Distribution Function Newtonian Number Density in Phase Space, N Relativistic Number Density in Phase Space, N 99 viii

3 3.2.3 Distribution Function f(x, v, t) for Particles in a Plasma Distribution Function I ν /ν 3 for Photons Mean Occupation Number η Thermal-Equilibrium Distribution Functions Macroscopic Properties of Matter as Integrals over Momentum Space Particle Density n, Flux S, and Stress Tensor T Relativistic Number-Flux 4-Vector S and Stress-Energy Tensor T Isotropic Distribution Functions and Equations of State Newtonian Density, Pressure, Energy Density, and Equation of State Equations of State for a Nonrelativistic Hydrogen Gas Relativistic Density, Pressure, Energy Density, and Equation of State Equation of State for a Relativistic Degenerate Hydrogen Gas Equation of State for Radiation Evolution of the Distribution Function: Liouville s Theorem, the Collisionless Boltzmann Equation, and the Boltzmann Transport Equation Transport Coefficients Diffusive Heat Conduction inside a Star Order-of-Magnitude Analysis Analysis Using the Boltzmann Transport Equation 144 Bibliographic Note Statistical Mechanics Overview Systems, Ensembles, and Distribution Functions Systems Ensembles Distribution Function Liouville s Theorem and the Evolution of the Distribution Function Statistical Equilibrium Canonical Ensemble and Distribution General Equilibrium Ensemble and Distribution; Gibbs Ensemble; Grand Canonical Ensemble Fermi-Dirac and Bose-Einstein Distributions Equipartition Theorem for Quadratic, Classical Degrees of Freedom The Microcanonical Ensemble The Ergodic Hypothesis Entropy and Evolution toward Statistical Equilibrium Entropy and the Second Law of Thermodynamics What Causes the Entropy to Increase? Entropy per Particle Bose-Einstein Condensate 193 ix

4 4.10 Statistical Mechanics in the Presence of Gravity Galaxies Black Holes The Universe Structure Formation in the Expanding Universe: Violent Relaxation and Phase Mixing Entropy and Information Information Gained When Measuring the State of a System in a Microcanonical Ensemble Information in Communication Theory Examples of Information Content Some Properties of Information Capacity of Communication Channels; Erasing Information from Computer Memories 216 Bibliographic Note Statistical Thermodynamics Overview Microcanonical Ensemble and the Energy Representation of Thermodynamics Extensive and Intensive Variables; Fundamental Potential Energy as a Fundamental Potential Intensive Variables Identified Using Measuring Devices; First Law of Thermodynamics Euler s Equation and Form of the Fundamental Potential Everything Deducible from First Law; Maxwell Relations Representations of Thermodynamics Grand Canonical Ensemble and the Grand-Potential Representation of Thermodynamics The Grand-Potential Representation, and Computation of Thermodynamic Properties as a Grand Canonical Sum Nonrelativistic van der Waals Gas Canonical Ensemble and the Physical-Free-Energy Representation of Thermodynamics Experimental Meaning of Physical Free Energy Ideal Gas with Internal Degrees of Freedom Gibbs Ensemble and Representation of Thermodynamics; Phase Transitions and Chemical Reactions Out-of-Equilibrium Ensembles and Their Fundamental Thermodynamic Potentials and Minimum Principles Phase Transitions Chemical Reactions Fluctuations away from Statistical Equilibrium 260 x

5 5.7 Van der Waals Gas: Volume Fluctuations and Gas-to-Liquid Phase Transition Magnetic Materials Paramagnetism; The Curie Law Ferromagnetism: The Ising Model Renormalization Group Methods for the Ising Model Monte Carlo Methods for the Ising Model 279 Bibliographic Note Random Processes Overview Fundamental Concepts Random Variables and Random Processes Probability Distributions Ergodic Hypothesis Markov Processes and Gaussian Processes Markov Processes; Random Walk Gaussian Processes and the Central Limit Theorem; Random Walk Doob s Theorem for Gaussian-Markov Processes, and Brownian Motion Correlation Functions and Spectral Densities Correlation Functions; Proof of Doob s Theorem Spectral Densities Physical Meaning of Spectral Density, Light Spectra, and Noise in a Gravitational Wave Detector The Wiener-Khintchine Theorem; Cosmological Density Fluctuations Dimensional Random Processes Cross Correlation and Correlation Matrix Spectral Densities and the Wiener-Khintchine Theorem Noise and Its Types of Spectra Shot Noise, Flicker Noise, and Random-Walk Noise; Cesium Atomic Clock Information Missing from Spectral Density Filtering Random Processes Filters, Their Kernels, and the Filtered Spectral Density Brownian Motion and Random Walks Extracting a Weak Signal from Noise: Band-Pass Filter, Wiener s Optimal Filter, Signal-to-Noise Ratio, and Allan Variance of Clock Noise Shot Noise Fluctuation-Dissipation Theorem Elementary Version of the Fluctuation-Dissipation Theorem; Langevin Equation, Johnson Noise in a Resistor, and Relaxation Time for Brownian Motion Generalized Fluctuation-Dissipation Theorem; Thermal Noise in a Laser Beam s Measurement of Mirror Motions; Standard Quantum Limit for Measurement Accuracy and How to Evade It 331 xi

6 6.9 Fokker-Planck Equation Fokker-Planck for a 1-Dimensional Markov Process Optical Molasses: Doppler Cooling of Atoms Fokker-Planck for a Multidimensional Markov Process; Thermal Noise in an Oscillator 343 Bibliographic Note 345 PART III OPTICS Geometric Optics Overview Waves in a Homogeneous Medium Monochromatic Plane Waves; Dispersion Relation Wave Packets Waves in an Inhomogeneous, Time-Varying Medium: The Eikonal Approximation and Geometric Optics Geometric Optics for a Prototypical Wave Equation Connection of Geometric Optics to Quantum Theory Geometric Optics for a General Wave Examples of Geometric-Optics Wave Propagation Relation to Wave Packets; Limitations of the Eikonal Approximation and Geometric Optics Fermat s Principle Paraxial Optics Axisymmetric, Paraxial Systems: Lenses, Mirrors, Telescopes, Microscopes, and Optical Cavities Converging Magnetic Lens for Charged Particle Beam Catastrophe Optics Image Formation Aberrations of Optical Instruments Gravitational Lenses Gravitational Deflection of Light Optical Configuration Microlensing Lensing by Galaxies Polarization Polarization Vector and Its Geometric-Optics Propagation Law Geometric Phase 406 Bibliographic Note 409 xii

7 8 Diffraction Overview Helmholtz-Kirchhoff Integral Diffraction by an Aperture Spreading of the Wavefront: Fresnel and Fraunhofer Regions Fraunhofer Diffraction Diffraction Grating Airy Pattern of a Circular Aperture: Hubble Space Telescope Babinet s Principle Fresnel Diffraction Rectangular Aperture, Fresnel Integrals, and the Cornu Spiral Unobscured Plane Wave Fresnel Diffraction by a Straight Edge: Lunar Occultation of a Radio Source Circular Apertures: Fresnel Zones and Zone Plates Paraxial Fourier Optics Coherent Illumination Point-Spread Functions Abbé s Description of Image Formation by a Thin Lens Image Processing by a Spatial Filter in the Focal Plane of a Lens: High-Pass, Low-Pass, and Notch Filters; Phase-Contrast Microscopy Gaussian Beams: Optical Cavities and Interferometric Gravitational-Wave Detectors Diffraction at a Caustic 451 Bibliographic Note Interference and Coherence Overview Coherence Young s Slits Interference with an Extended Source: Van Cittert-Zernike Theorem More General Formulation of Spatial Coherence; Lateral Coherence Length Generalization to 2 Dimensions Michelson Stellar Interferometer; Astronomical Seeing Temporal Coherence Michelson Interferometer and Fourier-Transform Spectroscopy Degree of Coherence; Relation to Theory of Random Processes Radio Telescopes Two-Element Radio Interferometer Multiple-Element Radio Interferometers Closure Phase Angular Resolution 482 xiii

8 9.4 Etalons and Fabry-Perot Interferometers Multiple-Beam Interferometry; Etalons Fabry-Perot Interferometer and Modes of a Fabry-Perot Cavity with Spherical Mirrors Fabry-Perot Applications: Spectrometer, Laser, Mode-Cleaning Cavity, Beam- Shaping Cavity, PDH Laser Stabilization, Optical Frequency Comb Laser Interferometer Gravitational-Wave Detectors Power Correlations and Photon Statistics: Hanbury Brown and Twiss Intensity Interferometer 509 Bibliographic Note Nonlinear Optics Overview Lasers Basic Principles of the Laser Types of Lasers and Their Performances and Applications Ti:Sapphire Mode-Locked Laser Free Electron Laser Holography Recording a Hologram Reconstructing the 3-Dimensional Image from a Hologram Other Types of Holography; Applications Phase-Conjugate Optics Maxwell s Equations in a Nonlinear Medium; Nonlinear Dielectric Susceptibilities; Electro-Optic Effects Three-Wave Mixing in Nonlinear Crystals Resonance Conditions for Three-Wave Mixing Three-Wave-Mixing Evolution Equations in a Medium That Is Dispersion-Free and Isotropic at Linear Order Three-Wave Mixing in a Birefringent Crystal: Phase Matching and Evolution Equations Applications of Three-Wave Mixing: Frequency Doubling, Optical Parametric Amplification, and Squeezed Light Frequency Doubling Optical Parametric Amplification Degenerate Optical Parametric Amplification: Squeezed Light Four-Wave Mixing in Isotropic Media Third-Order Susceptibilities and Field Strengths Phase Conjugation via Four-Wave Mixing in CS 2 Fluid Optical Kerr Effect and Four-Wave Mixing in an Optical Fiber 562 Bibliographic Note 564 xiv

9 PART IV ELASTICITY Elastostatics Overview Displacement and Strain Displacement Vector and Its Gradient Expansion, Rotation, Shear, and Strain Stress, Elastic Moduli, and Elastostatic Equilibrium Stress Tensor Realm of Validity for Hooke s Law Elastic Moduli and Elastostatic Stress Tensor Energy of Deformation Thermoelasticity Molecular Origin of Elastic Stress; Estimate of Moduli Elastostatic Equilibrium: Navier-Cauchy Equation Young s Modulus and Poisson s Ratio for an Isotropic Material: A Simple Elastostatics Problem Reducing the Elastostatic Equations to 1 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica Buckling and Bifurcation of Equilibria Elementary Theory of Buckling and Bifurcation Collapse of the World Trade Center Buildings Buckling with Lateral Force; Connection to Catastrophe Theory Other Bifurcations: Venus Fly Trap, Whirling Shaft, Triaxial Stars, and Onset of Turbulence Reducing the Elastostatic Equations to 2 Dimensions for a Deformed Thin Plate: Stress Polishing a Telescope Mirror Cylindrical and Spherical Coordinates: Connection Coefficients and Components of the Gradient of the Displacement Vector Solving the 3-Dimensional Navier-Cauchy Equation in Cylindrical Coordinates Simple Methods: Pipe Fracture and Torsion Pendulum Separation of Variables and Green s Functions: Thermoelastic Noise in Mirrors 622 Bibliographic Note Elastodynamics Overview Basic Equations of Elastodynamics; Waves in a Homogeneous Medium Equation of Motion for a Strained Elastic Medium Elastodynamic Waves Longitudinal Sound Waves 637 xv

10 Transverse Shear Waves Energy of Elastodynamic Waves Waves in Rods, Strings, and Beams Compression Waves in a Rod Torsion Waves in a Rod Waves on Strings Flexural Waves on a Beam Bifurcation of Equilibria and Buckling (Once More) Body Waves and Surface Waves Seismology and Ultrasound Body Waves Edge Waves Green s Function for a Homogeneous Half-Space Free Oscillations of Solid Bodies Seismic Tomography Ultrasound; Shock Waves in Solids The Relationship of Classical Waves to Quantum Mechanical Excitations 667 Bibliographic Note 670 PART V FLUID DYNAMICS Foundations of Fluid Dynamics Overview The Macroscopic Nature of a Fluid: Density, Pressure, Flow Velocity; Liquids versus Gases Hydrostatics Archimedes Law Nonrotating Stars and Planets Rotating Fluids Conservation Laws The Dynamics of an Ideal Fluid Mass Conservation Momentum Conservation Euler Equation Bernoulli s Theorem Conservation of Energy Incompressible Flows Viscous Flows with Heat Conduction Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear Navier-Stokes Equation Molecular Origin of Viscosity Energy Conservation and Entropy Production 714 xvi

11 Reynolds Number Pipe Flow Relativistic Dynamics of a Perfect Fluid Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets Nonrelativistic Limit of the Stress-Energy Tensor 723 Bibliographic Note Vorticity Overview Vorticity, Circulation, and Their Evolution Vorticity Evolution Barotropic, Inviscid, Compressible Flows: Vortex Lines Frozen into Fluid Tornados Circulation and Kelvin s Theorem Diffusion of Vortex Lines Sources of Vorticity Low-Reynolds-Number Flow Stokes Flow and Sedimentation Motivation: Climate Change Stokes Flow Sedimentation Rate High-Reynolds-Number Flow Laminar Boundary Layers Blasius Velocity Profile Near a Flat Plate: Stream Function and Similarity Solution Blasius Vorticity Profile Viscous Drag Force on a Flat Plate Boundary Layer Near a Curved Surface: Separation Nearly Rigidly Rotating Flows Earth s Atmosphere and Oceans Equations of Fluid Dynamics in a Rotating Reference Frame Geostrophic Flows Taylor-Proudman Theorem Ekman Boundary Layers Instabilities of Shear Flows Billow Clouds and Turbulence in the Stratosphere Discontinuous Flow: Kelvin-Helmholtz Instability Discontinuous Flow with Gravity Smoothly Stratified Flows: Rayleigh and Richardson Criteria for Instability 784 Bibliographic Note Turbulence Overview The Transition to Turbulence Flow Past a Cylinder 789 xvii

12 15.3 Empirical Description of Turbulence The Role of Vorticity in Turbulence Semiquantitative Analysis of Turbulence Weak-Turbulence Formalism Turbulent Viscosity Turbulent Wakes and Jets; Entrainment; the Coanda Effect Kolmogorov Spectrum for Fully Developed, Homogeneous, Isotropic Turbulence Turbulent Boundary Layers Profile of a Turbulent Boundary Layer Coanda Effect and Separation in a Turbulent Boundary Layer Instability of a Laminar Boundary Layer Flight of a Ball The Route to Turbulence Onset of Chaos Rotating Couette Flow Feigenbaum Sequence, Poincaré Maps, and the Period-Doubling Route to Turbulence in Convection Other Routes to Turbulent Convection Extreme Sensitivity to Initial Conditions 832 Bibliographic Note Waves Overview Gravity Waves on and beneath the Surface of a Fluid Deep-Water Waves and Their Excitation and Damping Shallow-Water Waves Capillary Waves and Surface Tension Helioseismology Nonlinear Shallow-Water Waves and Solitons Korteweg de Vries (KdV) Equation Physical Effects in the KdV Equation Single-Soliton Solution Two-Soliton Solution Solitons in Contemporary Physics Rossby Waves in a Rotating Fluid Sound Waves Wave Energy Sound Generation Radiation Reaction, Runaway Solutions, and Matched Asymptotic Expansions 869 Bibliographic Note 874 xviii

13 17 Compressible and Supersonic Flow Overview Equations of Compressible Flow Stationary, Irrotational, Quasi-1-Dimensional Flow Basic Equations; Transition from Subsonic to Supersonic Flow Setting up a Stationary, Transonic Flow Rocket Engines Dimensional, Time-Dependent Flow Riemann Invariants Shock Tube Shock Fronts Junction Conditions across a Shock; Rankine-Hugoniot Relations Junction Conditions for Ideal Gas with Constant γ Internal Structure of a Shock Mach Cone Self-Similar Solutions Sedov-Taylor Blast Wave The Sedov-Taylor Solution Atomic Bomb Supernovae 914 Bibliographic Note Convection Overview Diffusive Heat Conduction Cooling a Nuclear Reactor; Thermal Boundary Layers Boussinesq Approximation Rayleigh-Bénard Convection Convection in Stars Double Diffusion Salt Fingers 937 Bibliographic Note Magnetohydrodynamics Overview Basic Equations of MHD Maxwell s Equations in the MHD Approximation Momentum and Energy Conservation Boundary Conditions Magnetic Field and Vorticity Magnetostatic Equilibria Controlled Thermonuclear Fusion Z-Pinch 960 xix

14 Pinch Tokamak Hydromagnetic Flows Stability of Magnetostatic Equilibria Linear Perturbation Theory Z-Pinch: Sausage and Kink Instabilities The -Pinch and Its Toroidal Analog; Flute Instability; Motivation for Tokamak Energy Principle and Virial Theorems Dynamos and Reconnection of Magnetic Field Lines Cowling s Theorem Kinematic Dynamos Magnetic Reconnection Magnetosonic Waves and the Scattering of Cosmic Rays Cosmic Rays Magnetosonic Dispersion Relation Scattering of Cosmic Rays by Alfvén Waves 992 Bibliographic Note 993 PART VI PLASMA PHYSICS The Particle Kinetics of Plasma Overview Examples of Plasmas and Their Density-Temperature Regimes Ionization Boundary Degeneracy Boundary Relativistic Boundary Pair-Production Boundary Examples of Natural and Human-Made Plasmas Collective Effects in Plasmas Debye Shielding and Plasma Oscillations Debye Shielding Collective Behavior Plasma Oscillations and Plasma Frequency Coulomb Collisions Collision Frequency The Coulomb Logarithm Thermal Equilibration Rates in a Plasma Discussion Transport Coefficients Coulomb Collisions Anomalous Resistivity and Anomalous Equilibration 1016 xx

15 20.6 Magnetic Field Cyclotron Frequency and Larmor Radius Validity of the Fluid Approximation Conductivity Tensor Particle Motion and Adiabatic Invariants Homogeneous, Time-Independent Magnetic Field and No Electric Field Homogeneous, Time-Independent Electric and Magnetic Fields Inhomogeneous, Time-Independent Magnetic Field A Slowly Time-Varying Magnetic Field Failure of Adiabatic Invariants; Chaotic Orbits 1030 Bibliographic Note Waves in Cold Plasmas: Two-Fluid Formalism Overview Dielectric Tensor, Wave Equation, and General Dispersion Relation Two-Fluid Formalism Wave Modes in an Unmagnetized Plasma Dielectric Tensor and Dispersion Relation for a Cold, Unmagnetized Plasma Plasma Electromagnetic Modes Langmuir Waves and Ion-Acoustic Waves in Warm Plasmas Cutoffs and Resonances Wave Modes in a Cold, Magnetized Plasma Dielectric Tensor and Dispersion Relation Parallel Propagation Perpendicular Propagation Propagation of Radio Waves in the Ionosphere; Magnetoionic Theory CMA Diagram for Wave Modes in a Cold, Magnetized Plasma Two-Stream Instability 1065 Bibliographic Note Kinetic Theory of Warm Plasmas Overview Basic Concepts of Kinetic Theory and Its Relationship to Two-Fluid Theory Distribution Function and Vlasov Equation Relation of Kinetic Theory to Two-Fluid Theory Jeans Theorem Electrostatic Waves in an Unmagnetized Plasma: Landau Damping Formal Dispersion Relation Two-Stream Instability The Landau Contour Dispersion Relation for Weakly Damped or Growing Waves 1085 xxi

16 Langmuir Waves and Their Landau Damping Ion-Acoustic Waves and Conditions for Their Landau Damping to Be Weak Stability of Electrostatic Waves in Unmagnetized Plasmas Nyquist s Method Penrose s Instability Criterion Particle Trapping N-Particle Distribution Function BBGKY Hierarchy Two-Point Correlation Function Coulomb Correction to Plasma Pressure 1107 Bibliographic Note Nonlinear Dynamics of Plasmas Overview Quasilinear Theory in Classical Language Classical Derivation of the Theory Summary of Quasilinear Theory Conservation Laws Generalization to 3 Dimensions Quasilinear Theory in Quantum Mechanical Language Plasmon Occupation Number η Evolution of η for Plasmons via Interaction with Electrons Evolution of f for Electrons via Interaction with Plasmons Emission of Plasmons by Particles in the Presence of a Magnetic Field Relationship between Classical and Quantum Mechanical Formalisms Evolution of η via Three-Wave Mixing Quasilinear Evolution of Unstable Distribution Functions A Bump in the Tail Instability of Streaming Cosmic Rays Parametric Instabilities; Laser Fusion Solitons and Collisionless Shock Waves 1142 Bibliographic Note 1149 PART VII GENERAL RELATIVITY From Special to General Relativity Overview Special Relativity Once Again Geometric, Frame-Independent Formulation Inertial Frames and Components of Vectors, Tensors, and Physical Laws Light Speed, the Interval, and Spacetime Diagrams Differential Geometry in General Bases and in Curved Manifolds Nonorthonormal Bases 1161 xxii

17 Vectors as Directional Derivatives; Tangent Space; Commutators Differentiation of Vectors and Tensors; Connection Coefficients Integration The Stress-Energy Tensor Revisited The Proper Reference Frame of an Accelerated Observer Relation to Inertial Coordinates; Metric in Proper Reference Frame; Transport Law for Rotating Vectors Geodesic Equation for a Freely Falling Particle Uniformly Accelerated Observer Rindler Coordinates for Minkowski Spacetime 1187 Bibliographic Note Fundamental Concepts of General Relativity History and Overview Local Lorentz Frames, the Principle of Relativity, and Einstein s Equivalence Principle The Spacetime Metric, and Gravity as a Curvature of Spacetime Free-Fall Motion and Geodesics of Spacetime Relative Acceleration, Tidal Gravity, and Spacetime Curvature Newtonian Description of Tidal Gravity Relativistic Description of Tidal Gravity Comparison of Newtonian and Relativistic Descriptions Properties of the Riemann Curvature Tensor Delicacies in the Equivalence Principle, and Some Nongravitational Laws of Physics in Curved Spacetime Curvature Coupling in the Nongravitational Laws The Einstein Field Equation Geometrized Units Weak Gravitational Fields Newtonian Limit of General Relativity Linearized Theory Gravitational Field outside a Stationary, Linearized Source of Gravity Conservation Laws for Mass, Momentum, and Angular Momentum in Linearized Theory Conservation Laws for a Strong-Gravity Source 1238 Bibliographic Note Relativistic Stars and Black Holes Overview Schwarzschild s Spacetime Geometry The Schwarzschild Metric, Its Connection Coefficients, and Its Curvature Tensors 1242 xxiii

18 The Nature of Schwarzschild s Coordinate System, and Symmetries of the Schwarzschild Spacetime Schwarzschild Spacetime at Radii r M: The Asymptotically Flat Region Schwarzschild Spacetime at r M Static Stars Birkhoff s Theorem Stellar Interior Local Conservation of Energy and Momentum The Einstein Field Equation Stellar Models and Their Properties Embedding Diagrams Gravitational Implosion of a Star to Form a Black Hole The Implosion Analyzed in Schwarzschild Coordinates Tidal Forces at the Gravitational Radius Stellar Implosion in Eddington-Finkelstein Coordinates Tidal Forces at r = 0 The Central Singularity Schwarzschild Black Hole Spinning Black Holes: The Kerr Spacetime The Kerr Metric for a Spinning Black Hole Dragging of Inertial Frames The Light-Cone Structure, and the Horizon Evolution of Black Holes Rotational Energy and Its Extraction The Many-Fingered Nature of Time 1293 Bibliographic Note Gravitational Waves and Experimental Tests of General Relativity Overview Experimental Tests of General Relativity Equivalence Principle, Gravitational Redshift, and Global Positioning System Perihelion Advance of Mercury Gravitational Deflection of Light, Fermat s Principle, and Gravitational Lenses Shapiro Time Delay Geodetic and Lense-Thirring Precession Gravitational Radiation Reaction Gravitational Waves Propagating through Flat Spacetime Weak, Plane Waves in Linearized Theory Measuring a Gravitational Wave by Its Tidal Forces Gravitons and Their Spin and Rest Mass 1319 xxiv

19 27.4 Gravitational Waves Propagating through Curved Spacetime Gravitational Wave Equation in Curved Spacetime Geometric-Optics Propagation of Gravitational Waves Energy and Momentum in Gravitational Waves The Generation of Gravitational Waves Multipole-Moment Expansion Quadrupole-Moment Formalism Quadrupolar Wave Strength, Energy, Angular Momentum, and Radiation Reaction Gravitational Waves from a Binary Star System Gravitational Waves from Binaries Made of Black Holes, Neutron Stars, or Both: Numerical Relativity The Detection of Gravitational Waves Frequency Bands and Detection Techniques Gravitational-Wave Interferometers: Overview and Elementary Treatment Interferometer Analyzed in TT Gauge Interferometer Analyzed in the Proper Reference Frame of the Beam Splitter Realistic Interferometers Pulsar Timing Arrays 1355 Bibliographic Note Cosmology Overview General Relativistic Cosmology Isotropy and Homogeneity Geometry Kinematics Dynamics The Universe Today Baryons Dark Matter Photons Neutrinos Cosmological Constant Standard Cosmology Seven Ages of the Universe Particle Age Nuclear Age Photon Age 1392 xxv

20 Plasma Age Atomic Age Gravitational Age Cosmological Age Galaxy Formation Linear Perturbations Individual Constituents Solution of the Perturbation Equations Galaxies Cosmological Optics Cosmic Microwave Background Weak Gravitational Lensing Sunyaev-Zel dovich Effect Three Mysteries Inflation and the Origin of the Universe Dark Matter and the Growth of Structure The Cosmological Constant and the Fate of the Universe 1444 Bibliographic Note 1447 References 1449 Name Index 1473 Subject Index 1477 xxvi