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Princeton: Princeton University Press, 2017. — 1552 p.This first-year, graduate-level text and reference book covers the fundamental concepts and twenty-first-century applications of six major areas of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn't: statistical physics, optics (waves of all sorts), elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology. Growing out of a full-year course that the eminent researchers Kip Thorne and Roger Blandford taught at Caltech for almost three decades, this book is designed to broaden the training of physicists. Its six main topical sections are also designed so they can be used in separate courses, and the book provides an invaluable reference for researchers.

Presents all the major fields of classical physics except three prerequisites: classical mechanics, electromagnetism, and elementary thermodynamics

Elucidates the interconnections between diverse fields and explains their shared concepts and tools

Focuses on fundamental concepts and modern, real-world applications

Takes applications from fundamental, experimental, and applied physics; astrophysics and cosmology; geophysics, oceanography, and meteorology; biophysics and chemical physics; engineering and optical science and technology; and information science and technology

Emphasizes the quantum roots of classical physics and how to use quantum techniques to elucidate classical concepts or simplify classical calculations

Features hundreds of color figures, some five hundred exercises, extensive cross-references, and a detailed index

An online illustration package is available to professorsContents :Cover

Title

Copyright

Dedication

List of Boxes

Preface

Acknowledgments

PART I FOUNDATIONS

The Geometric Viewpoint on the Laws of Physics

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

Energy and Momentum of a Moving Particle

Bibliographic Note

Overview

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

Relativistic Particle Kinetics: World Lines, -Velocity, -Momentum and Its Conservation, Force

Geometric Derivation of the Lorentz Force Law

Index Gymnastics

Slot-Naming Notation

Particle Kinetics in Index Notation and in a Lorentz Frame

Lorentz Transformations

Spacetime Diagrams for Boosts

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

Spacetime Volumes and Integration

Conservation of Charge in Spacetime

Conservation of Particles, Baryon Number, and Rest Mass

Stress-Energy Tensor

-Momentum Conservation

Stress-Energy Tensors for Perfect Fluids and Electromagnetic Fields

Bibliographic Note

PART II STATISTICAL PHYSICS

Overview

Newtonian Number Density in Phase Space, N

Relativistic Number Density in Phase Space, N

Distribution Function f (x, v, t) for Particles in a Plasma

Distribution Function Iv/v^ for Photons

Mean Occupation Number n

Thermal-Equilibrium Distribution Functions

Particle Density n, Flux S, and Stress Tensor T

Relativistic Number-Flux -Vector S and Stress-Energy Tensor T

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

Bibliographic Note

Overview

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 the Second Law of Thermodynamics

What Causes the Entropy to Increase?

Entropy per Particle

Bose-Einstein Condensate

Galaxies

Black Holes

The Universe

Structure Formation in the Expanding Universe: Violent Relaxation and Phase Mixing

Information Gained When Measuring the State of a System in a Microcanonical Ensemble

Information in Communication Theory

Examples of Information Content

Capacity of Communication Channels; Erasing Information from Computer Memories

Bibliographic Note

Overview

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

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

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

Bibliographic Note

Overview

Random Variables and Random Processes

Probability Distributions

Ergodic Hypothesis

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; 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

Cross Correlation and Correlation Matrix

Spectral Densities and the Wiener-Khintchine Theorem

Shot Noise, Flicker Noise, and Random-Walk Noise; Cesium Atomic Clock

Information Missing from Spectral Density

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

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

Fokker-Planck Equation

Fokker-Planck for a -Dimensional Markov Process

Optical Molasses: Doppler Cooling of Atoms

Fokker-Planck for a Multidimensional Markov Process; Thermal Noise in an Oscillator

Bibliographic Note

PART III OPTICS

Overview

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

Image Formation

Aberrations of Optical Instruments

Gravitational Deflection of Light

Optical Configuration

Microlensing

Lensing by Galaxies

Polarization Vector and Its Geometric-Optics Propagation Law

Geometric Phase

Bibliographic Note

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

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

Bibliographic Note

Overview

Young’s Slits

Interference with an Extended Source: Van Cittert-Zernike Theorem

More General Formulation of Spatial Coherence; Lateral Coherence Length

Generalization to Dimensions

Michelson Stellar Interferometer; Astronomical Seeing

Temporal Coherence

Michelson Interferometer and Fourier-Transform Spectroscopy

Degree of Coherence; Relation to Theory of Random Processes

Two-Element Radio Interferometer

Multiple-Element Radio Interferometers

Closure Phase

Angular Resolution

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

Bibliographic Note

Overview

Basic Principles of the Laser

Types of Lasers and Their Performances and Applications

Ti:Sapphire Mode-Locked Laser

Holography

Recording a Hologram

Reconstructing the -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

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

Frequency Doubling

Optical Parametric Amplification

Degenerate Optical Parametric Amplification: Squeezed Light

Third-Order Susceptibilities and Field Strengths

Phase Conjugation via Four-Wave Mixing in CS Fluid

Optical Kerr Effect and Four-Wave Mixing in an Optical Fiber

Bibliographic Note

PART IV ELASTICITY

Overview

Displacement Vector and Its Gradient

Expansion, Rotation, Shear, and Strain

Stress Tensor

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 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica

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 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

Simple Methods: Pipe Fracture and Torsion Pendulum

Separation of Variables and Green’s Functions: Thermoelastic Noise in Mirrors

Bibliographic Note

Overview

Equation of Motion for a Strained Elastic Medium

Elastodynamic Waves

Longitudinal Sound Waves

Transverse Shear Waves

Energy of Elastodynamic Waves

Waves in Rods, Strings, and Beams

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

Ultrasound; Shock Waves in Solids

The Relationship of Classical Waves to Quantum Mechanical Excitations

Bibliographic Note

PART V 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

Momentum Conservation

Bernoulli’s Theorem

Conservation of Energy

Incompressible Flows

Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear

Navier-Stokes Equation

Molecular Origin of Viscosity

Energy Conservation and Entropy Production

Pipe Flow

Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics

Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets

Nonrelativistic Limit of the Stress-Energy Tensor

Bibliographic Note

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

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

Discontinuous Flow: Kelvin-Helmholtz Instability

Discontinuous Flow with Gravity

Smoothly Stratified Flows: Rayleigh and Richardson Criteria for Instability

Bibliographic Note

Overview

The Transition to Turbulence—Flow Past a Cylinder

Empirical Description of Turbulence

The Role of Vorticity in 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

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

Bibliographic Note

Overview

Gravity Waves on and beneath the Surface of a Fluid

Shallow-Water Waves

Capillary Waves and Surface Tension

Helioseismology

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

Bibliographic Note

Overview

Equations of Compressible Flow

Basic Equations; Transition from Subsonic to Supersonic Flow

Setting up a Stationary, Transonic Flow

Rocket Engines

Riemann Invariants

Shock Tube

Shock Fronts

Junction Conditions across a Shock; Rankine-Hugoniot Relations

Junction Conditions for Ideal Gas with Constant

Internal Structure of a Shock

Mach Cone

Self-Similar Solutions—Sedov-Taylor Blast Wave

The Sedov-Taylor Solution

Atomic Bomb

Supernovae

Bibliographic Note

Overview

Diffusive Heat Conduction—Cooling a Nuclear Reactor; Thermal Boundary Layers

Boussinesq Approximation

Rayleigh-Bénard Convection

Convection in Stars

Double Diffusion—Salt Fingers

Bibliographic Note

Overview

Basic Equations of MHD

Maxwell’s Equations in the MHD Approximation

Momentum and Energy Conservation

Boundary Conditions

Magnetic Field and Vorticity

Controlled Thermonuclear Fusion

Z-Pinch

Θ-Pinch

Tokamak

Hydromagnetic Flows

Linear Perturbation Theory

Z-Pinch: Sausage and Kink Instabilities

The Θ-Pinch and Its Toroidal Analog; Flute Instability; Motivation for Tokamak

Energy Principle and Virial Theorems

Cowling’s Theorem

Kinematic Dynamos

Magnetic Reconnection

Cosmic Rays

Magnetosonic Dispersion Relation

Scattering of Cosmic Rays by Alfvén Waves

Bibliographic Note

PART VI PLASMA PHYSICS

Overview

Ionization Boundary

Relativistic Boundary

Examples of Natural and Human-Made Plasmas

Debye Shielding

Collective Behavior

Plasma Oscillations and Plasma Frequency

Collision Frequency

The Coulomb Logarithm

Thermal Equilibration Rates in a Plasma

Discussion

Coulomb Collisions

Anomalous Resistivity and Anomalous Equilibration

Cyclotron Frequency and Larmor Radius

Validity of the Fluid Approximation

Conductivity Tensor

Particle Motion and Adiabatic Invariants

Homogeneous, Time-Independent Electric and Magnetic Fields

Inhomogeneous, Time-Independent Magnetic Field

A Slowly Time-Varying Magnetic Field

Failure of Adiabatic Invariants; Chaotic Orbits

Bibliographic Note

Overview

Dielectric Tensor, Wave Equation, and General Dispersion Relation

Two-Fluid Formalism

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

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

Bibliographic Note

Overview

Distribution Function and Vlasov Equation

Relation of Kinetic Theory to Two-Fluid Theory

Jeans’ Theorem

Formal Dispersion Relation

Two-Stream Instability

The Landau Contour

Dispersion Relation for Weakly Damped or Growing Waves

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

Penrose’s Instability Criterion

Particle Trapping

N-Particle Distribution Function

BBGKY Hierarchy

Two-Point Correlation Function

Coulomb Correction to Plasma Pressure

Bibliographic Note

Overview

Classical Derivation of the Theory

Summary of Quasilinear Theory

Conservation Laws

Generalization to Dimensions

Plasmon Occupation Number n

Evolution of n for Plasmons via Interaction with Electrons

Evolution of f for Electrons via Interaction with Plasmons

Relationship between Classical and Quantum Mechanical Formalisms

Evolution of n 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

Bibliographic Note

PART VII GENERAL RELATIVITY

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

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

Bibliographic Note

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

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

Bibliographic Note

Overview

The Schwarzschild Metric, Its Connection Coefficients, and Its Curvature Tensors

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

Birkhoff’s Theorem

Stellar Interior

Local Conservation of Energy and Momentum

The Einstein Field Equation

Stellar Models and Their Properties

Embedding Diagrams

The Implosion Analyzed in Schwarzschild Coordinates

Tidal Forces at the Gravitational Radius

Stellar Implosion in Eddington-Finkelstein Coordinates

Tidal Forces at r = —The Central Singularity

Schwarzschild Black Hole

The Kerr Metric for a Spinning Black Hole

The Light-Cone Structure, and the Horizon

Evolution of Black Holes—Rotational Energy and Its Extraction

The Many-Fingered Nature of Time

Bibliographic Note

Overview

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

Weak, Plane Waves in Linearized Theory

Measuring a Gravitational Wave by Its Tidal Forces

Gravitons and Their Spin and Rest Mass

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

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

Pulsar Timing Arrays

Bibliographic Note

Overview

Isotropy and Homogeneity

Geometry

Kinematics

Dynamics

Baryons

Dark Matter

Photons

Cosmological Constant

Seven Ages of the Universe

Particle Age

Nuclear Age

Photon Age

Plasma Age

Gravitational Age

Cosmological Age

Linear Perturbations

Individual Constituents

Solution of the Perturbation Equations

Galaxies

Cosmic Microwave Background

Weak Gravitational Lensing

Sunyaev-Zel’dovich Effect

Inflation and the Origin of the Universe

Dark Matter and the Growth of Structure

The Cosmological Constant and the Fate of the Universe

Bibliographic Note

References

Name Index

Subject Index

Presents all the major fields of classical physics except three prerequisites: classical mechanics, electromagnetism, and elementary thermodynamics

Elucidates the interconnections between diverse fields and explains their shared concepts and tools

Focuses on fundamental concepts and modern, real-world applications

Takes applications from fundamental, experimental, and applied physics; astrophysics and cosmology; geophysics, oceanography, and meteorology; biophysics and chemical physics; engineering and optical science and technology; and information science and technology

Emphasizes the quantum roots of classical physics and how to use quantum techniques to elucidate classical concepts or simplify classical calculations

Features hundreds of color figures, some five hundred exercises, extensive cross-references, and a detailed index

An online illustration package is available to professorsContents :Cover

Title

Copyright

Dedication

List of Boxes

Preface

Acknowledgments

PART I FOUNDATIONS

The Geometric Viewpoint on the Laws of Physics

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

Energy and Momentum of a Moving Particle

Bibliographic Note

Overview

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

Relativistic Particle Kinetics: World Lines, -Velocity, -Momentum and Its Conservation, Force

Geometric Derivation of the Lorentz Force Law

Index Gymnastics

Slot-Naming Notation

Particle Kinetics in Index Notation and in a Lorentz Frame

Lorentz Transformations

Spacetime Diagrams for Boosts

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

Spacetime Volumes and Integration

Conservation of Charge in Spacetime

Conservation of Particles, Baryon Number, and Rest Mass

Stress-Energy Tensor

-Momentum Conservation

Stress-Energy Tensors for Perfect Fluids and Electromagnetic Fields

Bibliographic Note

PART II STATISTICAL PHYSICS

Overview

Newtonian Number Density in Phase Space, N

Relativistic Number Density in Phase Space, N

Distribution Function f (x, v, t) for Particles in a Plasma

Distribution Function Iv/v^ for Photons

Mean Occupation Number n

Thermal-Equilibrium Distribution Functions

Particle Density n, Flux S, and Stress Tensor T

Relativistic Number-Flux -Vector S and Stress-Energy Tensor T

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

Bibliographic Note

Overview

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 the Second Law of Thermodynamics

What Causes the Entropy to Increase?

Entropy per Particle

Bose-Einstein Condensate

Galaxies

Black Holes

The Universe

Structure Formation in the Expanding Universe: Violent Relaxation and Phase Mixing

Information Gained When Measuring the State of a System in a Microcanonical Ensemble

Information in Communication Theory

Examples of Information Content

Capacity of Communication Channels; Erasing Information from Computer Memories

Bibliographic Note

Overview

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

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

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

Bibliographic Note

Overview

Random Variables and Random Processes

Probability Distributions

Ergodic Hypothesis

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; 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

Cross Correlation and Correlation Matrix

Spectral Densities and the Wiener-Khintchine Theorem

Shot Noise, Flicker Noise, and Random-Walk Noise; Cesium Atomic Clock

Information Missing from Spectral Density

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

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

Fokker-Planck Equation

Fokker-Planck for a -Dimensional Markov Process

Optical Molasses: Doppler Cooling of Atoms

Fokker-Planck for a Multidimensional Markov Process; Thermal Noise in an Oscillator

Bibliographic Note

PART III OPTICS

Overview

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

Image Formation

Aberrations of Optical Instruments

Gravitational Deflection of Light

Optical Configuration

Microlensing

Lensing by Galaxies

Polarization Vector and Its Geometric-Optics Propagation Law

Geometric Phase

Bibliographic Note

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

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

Bibliographic Note

Overview

Young’s Slits

Interference with an Extended Source: Van Cittert-Zernike Theorem

More General Formulation of Spatial Coherence; Lateral Coherence Length

Generalization to Dimensions

Michelson Stellar Interferometer; Astronomical Seeing

Temporal Coherence

Michelson Interferometer and Fourier-Transform Spectroscopy

Degree of Coherence; Relation to Theory of Random Processes

Two-Element Radio Interferometer

Multiple-Element Radio Interferometers

Closure Phase

Angular Resolution

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

Bibliographic Note

Overview

Basic Principles of the Laser

Types of Lasers and Their Performances and Applications

Ti:Sapphire Mode-Locked Laser

Holography

Recording a Hologram

Reconstructing the -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

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

Frequency Doubling

Optical Parametric Amplification

Degenerate Optical Parametric Amplification: Squeezed Light

Third-Order Susceptibilities and Field Strengths

Phase Conjugation via Four-Wave Mixing in CS Fluid

Optical Kerr Effect and Four-Wave Mixing in an Optical Fiber

Bibliographic Note

PART IV ELASTICITY

Overview

Displacement Vector and Its Gradient

Expansion, Rotation, Shear, and Strain

Stress Tensor

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 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica

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 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

Simple Methods: Pipe Fracture and Torsion Pendulum

Separation of Variables and Green’s Functions: Thermoelastic Noise in Mirrors

Bibliographic Note

Overview

Equation of Motion for a Strained Elastic Medium

Elastodynamic Waves

Longitudinal Sound Waves

Transverse Shear Waves

Energy of Elastodynamic Waves

Waves in Rods, Strings, and Beams

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

Ultrasound; Shock Waves in Solids

The Relationship of Classical Waves to Quantum Mechanical Excitations

Bibliographic Note

PART V 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

Momentum Conservation

Bernoulli’s Theorem

Conservation of Energy

Incompressible Flows

Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear

Navier-Stokes Equation

Molecular Origin of Viscosity

Energy Conservation and Entropy Production

Pipe Flow

Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics

Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets

Nonrelativistic Limit of the Stress-Energy Tensor

Bibliographic Note

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

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

Discontinuous Flow: Kelvin-Helmholtz Instability

Discontinuous Flow with Gravity

Smoothly Stratified Flows: Rayleigh and Richardson Criteria for Instability

Bibliographic Note

Overview

The Transition to Turbulence—Flow Past a Cylinder

Empirical Description of Turbulence

The Role of Vorticity in 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

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

Bibliographic Note

Overview

Gravity Waves on and beneath the Surface of a Fluid

Shallow-Water Waves

Capillary Waves and Surface Tension

Helioseismology

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

Bibliographic Note

Overview

Equations of Compressible Flow

Basic Equations; Transition from Subsonic to Supersonic Flow

Setting up a Stationary, Transonic Flow

Rocket Engines

Riemann Invariants

Shock Tube

Shock Fronts

Junction Conditions across a Shock; Rankine-Hugoniot Relations

Junction Conditions for Ideal Gas with Constant

Internal Structure of a Shock

Mach Cone

Self-Similar Solutions—Sedov-Taylor Blast Wave

The Sedov-Taylor Solution

Atomic Bomb

Supernovae

Bibliographic Note

Overview

Diffusive Heat Conduction—Cooling a Nuclear Reactor; Thermal Boundary Layers

Boussinesq Approximation

Rayleigh-Bénard Convection

Convection in Stars

Double Diffusion—Salt Fingers

Bibliographic Note

Overview

Basic Equations of MHD

Maxwell’s Equations in the MHD Approximation

Momentum and Energy Conservation

Boundary Conditions

Magnetic Field and Vorticity

Controlled Thermonuclear Fusion

Z-Pinch

Θ-Pinch

Tokamak

Hydromagnetic Flows

Linear Perturbation Theory

Z-Pinch: Sausage and Kink Instabilities

The Θ-Pinch and Its Toroidal Analog; Flute Instability; Motivation for Tokamak

Energy Principle and Virial Theorems

Cowling’s Theorem

Kinematic Dynamos

Magnetic Reconnection

Cosmic Rays

Magnetosonic Dispersion Relation

Scattering of Cosmic Rays by Alfvén Waves

Bibliographic Note

PART VI PLASMA PHYSICS

Overview

Ionization Boundary

Relativistic Boundary

Examples of Natural and Human-Made Plasmas

Debye Shielding

Collective Behavior

Plasma Oscillations and Plasma Frequency

Collision Frequency

The Coulomb Logarithm

Thermal Equilibration Rates in a Plasma

Discussion

Coulomb Collisions

Anomalous Resistivity and Anomalous Equilibration

Cyclotron Frequency and Larmor Radius

Validity of the Fluid Approximation

Conductivity Tensor

Particle Motion and Adiabatic Invariants

Homogeneous, Time-Independent Electric and Magnetic Fields

Inhomogeneous, Time-Independent Magnetic Field

A Slowly Time-Varying Magnetic Field

Failure of Adiabatic Invariants; Chaotic Orbits

Bibliographic Note

Overview

Dielectric Tensor, Wave Equation, and General Dispersion Relation

Two-Fluid Formalism

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

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

Bibliographic Note

Overview

Distribution Function and Vlasov Equation

Relation of Kinetic Theory to Two-Fluid Theory

Jeans’ Theorem

Formal Dispersion Relation

Two-Stream Instability

The Landau Contour

Dispersion Relation for Weakly Damped or Growing Waves

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

Penrose’s Instability Criterion

Particle Trapping

N-Particle Distribution Function

BBGKY Hierarchy

Two-Point Correlation Function

Coulomb Correction to Plasma Pressure

Bibliographic Note

Overview

Classical Derivation of the Theory

Summary of Quasilinear Theory

Conservation Laws

Generalization to Dimensions

Plasmon Occupation Number n

Evolution of n for Plasmons via Interaction with Electrons

Evolution of f for Electrons via Interaction with Plasmons

Relationship between Classical and Quantum Mechanical Formalisms

Evolution of n 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

Bibliographic Note

PART VII GENERAL RELATIVITY

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

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

Bibliographic Note

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

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

Bibliographic Note

Overview

The Schwarzschild Metric, Its Connection Coefficients, and Its Curvature Tensors

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

Birkhoff’s Theorem

Stellar Interior

Local Conservation of Energy and Momentum

The Einstein Field Equation

Stellar Models and Their Properties

Embedding Diagrams

The Implosion Analyzed in Schwarzschild Coordinates

Tidal Forces at the Gravitational Radius

Stellar Implosion in Eddington-Finkelstein Coordinates

Tidal Forces at r = —The Central Singularity

Schwarzschild Black Hole

The Kerr Metric for a Spinning Black Hole

The Light-Cone Structure, and the Horizon

Evolution of Black Holes—Rotational Energy and Its Extraction

The Many-Fingered Nature of Time

Bibliographic Note

Overview

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

Weak, Plane Waves in Linearized Theory

Measuring a Gravitational Wave by Its Tidal Forces

Gravitons and Their Spin and Rest Mass

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

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

Pulsar Timing Arrays

Bibliographic Note

Overview

Isotropy and Homogeneity

Geometry

Kinematics

Dynamics

Baryons

Dark Matter

Photons

Cosmological Constant

Seven Ages of the Universe

Particle Age

Nuclear Age

Photon Age

Plasma Age

Gravitational Age

Cosmological Age

Linear Perturbations

Individual Constituents

Solution of the Perturbation Equations

Galaxies

Cosmic Microwave Background

Weak Gravitational Lensing

Sunyaev-Zel’dovich Effect

Inflation and the Origin of the Universe

Dark Matter and the Growth of Structure

The Cosmological Constant and the Fate of the Universe

Bibliographic Note

References

Name Index

Subject Index

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