Gravitation

Cover......Page 0001.djvu
Gravitation......Page 0006.djvu
ISBN 0716703343......Page 0007.djvu
Preface......Page 0010.djvu
Contents......Page 0014.djvu
BOXES......Page 0024.djvu
FIGURES......Page 0027.djvu
ACKNOWLEDGMENTS......Page 0030.djvu
Part I. SPACETIME PHYSICS......Page 0034.djvu
1 The Parable of the Apple......Page 0036.djvu
2 Spacetime With and Without Coordinates......Page 0038.djvu
3 Weightlessness......Page 0046.djvu
4 Local Lorentz Geometry, With and Without Coordinates......Page 0052.djvu
5 Time......Page 0056.djvu
6 Curvature......Page 0062.djvu
7 Effect of Matter on Geometry......Page 0070.djvu
Part II. PHYSICS IN FLAT SPACETIME......Page 0078.djvu
1 Overview......Page 0080.djvu
2 Geometric Objects......Page 0081.djvu
3 Vectors......Page 0082.djvu
4 The Metric Tensor......Page 0084.djvu
5 Differential Forms......Page 0086.djvu
6 Gradients and Directional Derivatives......Page 0092.djvu
7 Coordinate Representation of Geometric Objects......Page 0093.djvu
8 The Centrifuge and the Photon......Page 0096.djvu
9 Lorentz Transformations......Page 0099.djvu
10 Collisions......Page 0102.djvu
1 The Lorentz Force and the Electromagnetic Field Tensor......Page 0104.djvu
2 Tensors in All Generality......Page 0107.djvu
3 Three-Plus-One View Versus Geometric View......Page 0111.djvu
4 Maxwell\'s Equations......Page 0112.djvu
5 Working with Tensors......Page 0114.djvu
1 Exterior Calculus......Page 0123.djvu
2 Electromagnetic 2-Form and Lorentz Force......Page 0132.djvu
3 Forms Illuminate Electromagnetism and Electromagnetism Illuminates Forms......Page 0138.djvu
4 Radiation Fields......Page 0143.djvu
5 Maxwell\'s Equations......Page 0145.djvu
6 Exterior Derivative and Closed Forms......Page 0147.djvu
7 Distant Action from Local Law......Page 0153.djvu
2 Three-Dimensional Volumes and Definition of the Stress-Energy Tensor......Page 0163.djvu
3 Components of Stress-Energy Tensor......Page 0170.djvu
4 Stress-Energy Tensor for a Swarm of Particles......Page 0171.djvu
5 Stress-Energy Tensor for a Perfect Fluid......Page 0172.djvu
6 Electromagnetic Stress-Energy......Page 0173.djvu
7 Symmetry of the Stress-Energy Tensor......Page 0174.djvu
8 Conservation of 4-Momentum. Integral Formulation......Page 0175.djvu
9 Conservation of 4-Momentum: Differential Formulation......Page 0179.djvu
10 Sample Application of nabla  T = 0......Page 0185.djvu
11 Angular Momentum......Page 0189.djvu
1 Accelerated Observers Can Be Analyzed Using Special Relativity......Page 0196.djvu
2 Hyperbolic Motion......Page 0199.djvu
3 Constraints on Size of an Accelerated Frame......Page 0201.djvu
4 The Tetrad Carried by a Uniformly Accelerated Observer......Page 0202.djvu
5 The Tetrad Fermi-Walker Transported by an Observer with Arbitrary Acceleration......Page 0203.djvu
6 The Local Coordinate System of an Accelerated Observer......Page 0205.djvu
1 Attempts to Incorporate Gravity Into Special Relativity......Page 0210.djvu
3 Gravitational Redshift Implies Spacetime Is Curved......Page 0220.djvu
4 Gravitational Redshift as Evidence for the Principle of Equivalence......Page 0222.djvu
5 Local Flatness, Global Curvature......Page 0223.djvu
Part III. THE MATHEMATICS OF CURVED SPACETIME......Page 0226.djvu
1 An Overview of Part III......Page 0228.djvu
2 Track 1 Versus Track 2: Difference In Outlook and Power......Page 0230.djvu
3 Three Aspects of Geometry Pictorial, Abstract, Component......Page 0231.djvu
4 Tensor Algebra In Curved Spacetime......Page 0234.djvu
5 Parallel Transport, Covariant Derivative, Connection Coefficients, Geodesics......Page 0240.djvu
6 Local Lorentz Frames Mathematical Discussion......Page 0250.djvu
7 Geodesic Deviation and the Riemann Curvature Tensor......Page 0251.djvu
1 Geometric Objects In Metric-Free, Geodesic-Free Spacetime......Page 0258.djvu
2 \"Vector\" and \"Directional Derivative\" Refined into Tangent Vector......Page 0259.djvu
3 Bases, Components, and Transformation Laws for Vectors......Page 0263.djvu
4 1-Forms......Page 0264.djvu
5 Tensors......Page 0266.djvu
6 Commutators and Pictorial Techniques......Page 0268.djvu
7 Manifolds and Differential Topology......Page 0273.djvu
1 Geodesics and the Equivalence Principle......Page 0277.djvu
2 Parallel Transport and Covariant Derivative: Pictorial Approach......Page 0278.djvu
3 Parallel Transport and Covariant Derivative: Abstract Approach......Page 0280.djvu
4 Parallel Transport and Covariant Derivative: Component Approach......Page 0291.djvu
5 Geodesic Equation......Page 0295.djvu
2 The Relative Acceleration of Neighboring Geodesics......Page 0298.djvu
3 Tidal Gravitational Forces and Riemann Curvature Tensor......Page 0303.djvu
4 Parallel Transport Around a Closed Curve......Page 0310.djvu
5 Flatness is Equivalent to Zero Riemann Curvature......Page 0316.djvu
6 Riemann Normal Coordinates......Page 0318.djvu
1 Newtonian Gravity in Brief......Page 0322.djvu
2 Stratification of Newtonian Spacetime......Page 0324.djvu
3 Galilean Coordinate Systems......Page 0325.djvu
4 Geometric, Coordinate-Free Formulation of Newtonian Gravity......Page 0331.djvu
5 The Geometric View of Physics: A Critique......Page 0335.djvu
1 New Features Imposed on Geometry by Local Validity of Special Relativity......Page 0337.djvu
2 Metric......Page 0338.djvu
3 Concord Between Geodesics of Curved Spacetime Geometry and Straight Lines of Local Lorentz Geometry......Page 0345.djvu
4 Geodesics as World Lines of Extremal Proper Time......Page 0348.djvu
5 Metric-Induced Properties of Riemann......Page 0357.djvu
6 The Proper Reference Frame of an Accelerated Observer......Page 0360.djvu
1 Curvature as a Tool for Understanding Physics......Page 0366.djvu
2 Forming the Einstein Tensor......Page 0376.djvu
4 The Geodesic Lagrangian Method......Page 0377.djvu
5 Curvature 2-Forms......Page 0381.djvu
6 Computation of Curvature Using Exterior Differential Forms......Page 0387.djvu
1 Bianchi Identities in Brief......Page 0397.djvu
2 Bianchi Identity dR = 0 as a Manifestation of \"Boundary of Boundary = 0\"......Page 0405.djvu
3 Moment of Rotation Key to Contracted Bianchi Identity......Page 0406.djvu
4 Calculation of the Moment of Rotation......Page 0408.djvu
5 Conservation of Moment of Rotation Seen from \"Boundary of a Boundary IS Zero\"......Page 0410.djvu
6 Conservation of Moment of Rotation Expressed in Differential Form......Page 0411.djvu
7 From Conservation of Moment of Rotation to Einstein\'s Geometrodynamics: A Preview......Page 0412.djvu
Part IV. EINSTEIN\'S GEOMETRIC THEORY OF GRAVITY......Page 0416.djvu
2 The Laws of Physics in Curved Spacetime......Page 0418.djvu
3 Factor-Ordenng Problems in the Equivalence Princlple......Page 0421.djvu
4 The Rods and Clocks Used to Measure Space and Time Intervals......Page 0426.djvu
5 The Measurement of the Gravitational Field......Page 0432.djvu
1 Automatic Conservation of the Source as the Central Idea in the Formulation of the Field Equation......Page 0437.djvu
2 Automatic Conservation of the Source A Dynamic Necessity......Page 0441.djvu
3 Cosmological Constant......Page 0442.djvu
4 The Newtonian Limit......Page 0445.djvu
5 Axiomatlze Einstein\'s Theory?......Page 0449.djvu
6 \"No Prior Geometry\". A Feature Distinguishing Einstein\'s Theory from Other Theories of Gravity......Page 0462.djvu
7 A Taste of the History of Einstein\'s Equation......Page 0464.djvu
1 The Linearized Theory of GravIty......Page 0468.djvu
3 Effect of Gravity on Matter......Page 0475.djvu
4 Nearly Newtonian Gravitational Fields......Page 0478.djvu
1 External Field of a Weakly Gravitating Source......Page 0481.djvu
2 Measurement of the Mass and Angular Momentum......Page 0483.djvu
3 Mass and Angular Momentum of Fully Relativistic Sources......Page 0484.djvu
4 Mass and Angular Momentum of a Closed Universe......Page 0490.djvu
1 Overview......Page 0493.djvu
2 Gaussian Flux Integrals for 4-Momentum and Angular Momentum......Page 0494.djvu
3 Volume Integrals for 4-Momentum and Angular Momentum......Page 0497.djvu
4 Why the Energy of the Gravitational Field Cannot be Localized......Page 0499.djvu
5 ConservatIon Laws for Total 4-Momentum and Angular Momentum......Page 0501.djvu
6 Equation of Motion Derived from the Field Equation......Page 0504.djvu
1 Dynamics Requires Initial-Value Data......Page 0517.djvu
2 The Hilbert Action Principle and the Palatini Method of Variation......Page 0524.djvu
3 Matter Lagrangian and Stress-Energy Tensor......Page 0537.djvu
4 Splitting Spacetime Into Space and Time......Page 0538.djvu
5 Intrinsic and Extrinsic Curvature......Page 0542.djvu
6 The Hilbert Action Principle and the Arnowitt-Deser-Misner Modification Thereof in the Space-plus-Time Split......Page 0552.djvu
7 The Arnowitt-Deser-Misner Formulation of the Dynamics of Geometry......Page 0553.djvu
8 Integrating Forward in Time......Page 0559.djvu
9 The Initial-Value Problem in the Thin-Sandwich Formulation......Page 0561.djvu
10 The Time-Symmetric and Time-Antisymmetric Initial-Value Problem......Page 0568.djvu
11 York\'s \"Handles\" to Specify a 4-Geometry......Page 0572.djvu
12 Mach\'s Principle and the Origin of Inertia......Page 0576.djvu
13 Junction Conditions......Page 0584.djvu
2 Thermodynamics in Curved Spacetime......Page 0590.djvu
3 Hydrodynamics in Curved Spacetime......Page 0595.djvu
4 Electrodynamics in Curved Spacetime......Page 0601.djvu
5 Geometric Optics in Curved Spacetime......Page 0603.djvu
6 Kinetic Theory in Curved Spacetime......Page 0616.djvu
Part V. RELATIVISTIC STARS......Page 0624.djvu
1 Prolog......Page 0626.djvu
2 Coordinates and Metric for a Static, Sphencal System......Page 0627.djvu
3 Physical Interpretation of Schwarzschild coordinates......Page 0628.djvu
4 Description of the Matter Inside a Star......Page 0630.djvu
5 Equations of Structure......Page 0633.djvu
6 External Gravitational Field......Page 0640.djvu
7 How to Construct a Stellar Model......Page 0641.djvu
8 The Spacetime Geometry for a Static Star......Page 0645.djvu
1 Overview......Page 0651.djvu
2 The Endpoint of Stellar Evolution......Page 0654.djvu
3 Pulsars......Page 0660.djvu
4 Supermasslve Stars and Stellar Instabilities......Page 0663.djvu
6 Relativistic Star Clusters......Page 0667.djvu
1 From Kepler\'s Laws to the Effective Potential for Motion In Schwarzschild Geometry......Page 0669.djvu
2 Symmetries and Conservation Laws......Page 0683.djvu
3 Conserved Quantities for Motion In Schwarzschild Geometry......Page 0688.djvu
5 Orbits of Particles......Page 0692.djvu
6 Orbit of a Photon, Neutrino, or Gravlton in Schwarzschild Geometry......Page 0705.djvu
7 Spherical Star Clusters......Page 0712.djvu
1 Motivation......Page 0721.djvu
2 Setting Up the Problem......Page 0722.djvu
3 Eulenan versus Lagrangian Perturbations......Page 0723.djvu
4 Initial-Value Equations......Page 0724.djvu
5 Dynamic Equation and Boundary Conditions......Page 0726.djvu
6 Summary of Results......Page 0727.djvu
Part VI. THE UNIVERSE......Page 0734.djvu
1 The Homogeneity and Isotropy of the Universe......Page 0736.djvu
2 Stress-Energy Content of the Universe-the Fluid Idealization......Page 0744.djvu
3 Geometric Implications of Homogeneity and Isotropy......Page 0746.djvu
4 Comoving, Synchronous Coordinate Systems for the Universe......Page 0748.djvu
5 The Expansion Factor......Page 0751.djvu
6 Possible 3-Geometries for a Hypersurface of Homogeneity......Page 0753.djvu
7 Equations of Motion for the Fluid......Page 0759.djvu
8 The Einstein Field Equations......Page 0761.djvu
9 Time Parameters and the Hubble Constant......Page 0763.djvu
10 The Elementary Friedmann Cosmology of a Closed Universe......Page 0766.djvu
11 Homogeneous Isotropic Model Universes that Violate Einstein\'s Conception of Cosmology......Page 0775.djvu
1 The \"Standard Model\" of the Universe......Page 0796.djvu
3 What\" Preceded\" the Initial Singularity?......Page 0802.djvu
4 Other Cosmological Theories......Page 0803.djvu
1 Parameters that Determine the Fate of the Universe......Page 0804.djvu
2 Cosmological Redshift......Page 0805.djvu
3 The Dlstance-Redshift Relation Measurement of the Hubble Constant......Page 0813.djvu
4 The Magnitude-Redshift Relation Measurement of the Deceleration Parameter......Page 0815.djvu
5 Search for \"Lens Effect\" of the Universe......Page 0828.djvu
6 Density of the Universe Today......Page 0829.djvu
7 Summary of Present Knowledge About Cosmological Parameters......Page 0830.djvu
1 Why is the Universe So Homogeneous and Isotropic?......Page 0833.djvu
2 The Kasner Model for an Anisotropic Universe......Page 0834.djvu
4 Viscous Dissipation of Anisotropy......Page 0835.djvu
5 Particle Creation in an Anisotropic Universe......Page 0836.djvu
6 Inhomogeneous Cosmologies......Page 0837.djvu
7 The Mixmaster Universe......Page 0838.djvu
8 Horizons and the Isotropy of the Microwave Background......Page 0848.djvu
Part VII. GRAVITATIONAL COLLAPSE AND BLACK HOLES......Page 0850.djvu
1 Inevitability of Collapse for Massive Stars......Page 0852.djvu
2 The Nonsingularity of the Gravitational Radius......Page 0853.djvu
3 Behavior of Schwarzschild Coordinates at r = 2M......Page 0856.djvu
4 Several Well-Behaved Coordinate Systems......Page 0859.djvu
5 Relationship Between Kruskal-Szekeres Coordinates and Schwarzschild Coordinates......Page 0866.djvu
6 Dynamics of the Schwarzschild Geometry......Page 0869.djvu
1 Relevance of Schwarzschild Geometry......Page 0875.djvu
2 Birkhoff\'s Theorem......Page 0876.djvu
3 Exterior Geometry of a Collapsing Star......Page 0879.djvu
4 Collapse of a Star with Uniform Density and Zero Pressure......Page 0884.djvu
5 Spherically Symmetric Collapse with Internal Pressure Forces......Page 0890.djvu
6 The Fate of a Man Who Falls into the Singularity at r = 0......Page 0893.djvu
7 Realistic Gravitational Collapse: An Overview......Page 0895.djvu
1 Why \"Black Hole\"?......Page 0905.djvu
2 The Gravitational and Electromagnetic Fields of a Black Hole......Page 0908.djvu
3 Mass, Angular Momentum, Charge, and Magnetic Moment......Page 0924.djvu
4 Symmetries and Frame Dragging......Page 0925.djvu
5 Equations of Motion for Test Particles......Page 0930.djvu
6 Principal Null Congruences......Page 0934.djvu
7 Storage and Removal of Energy from Black Holes......Page 0937.djvu
8 Reversible and Irreversible Transformations......Page 0940.djvu
1 Global Techniques Versus Local Techniques......Page 0949.djvu
2 \"Infinity\" in Asymptotically Flat Spacetime......Page 0950.djvu
3 Causality and Horizons......Page 0955.djvu
4 Global Structure of Horizons......Page 0957.djvu
5 Proof of Second Law of Black-Hole Dynamics......Page 0964.djvu
6 Singularity Theorems and the \"Issue of the Final State\"......Page 0967.djvu
Part VIII. GRAVITATIONAL WAVES......Page 0974.djvu
1 Viewpoints......Page 0976.djvu
2 Review of \"Linearized Theory\" in Vacuum......Page 0977.djvu
3 Plane-Wave Solutions in Linearized Theory......Page 0978.djvu
4 The Transverse Traceless (TT) Gauge......Page 0979.djvu
5 Geodesic Deviation in a Linearized Gravitational Wave......Page 0983.djvu
6 Polarization of a Plane Wave......Page 0985.djvu
7 The Stress-Energy Carried by a Gravitational Wave......Page 0988.djvu
8 Gravitational Waves in the Full Theory of General Relativity......Page 0989.djvu
9 An Exact Plane-Wave Solution......Page 0990.djvu
10 Physical Properties of the Exact Plane Wave......Page 0993.djvu
11 Comparison of an Exact Electromagnetic Plane Wave with the Gravitational Plane Wave......Page 0994.djvu
12 A New Viewpoint on the Exact Plane Wave......Page 0995.djvu
13 The Shortwave Approximation......Page 0997.djvu
14 Effect of Background Curvature on Wave Propagation......Page 1000.djvu
15 Stress-Energy Tensor for Gravitational Waves......Page 1002.djvu
1 The Quadrupole Nature of Gravitational Waves......Page 1007.djvu
2 Power Radiated in Terms of Internal Power Flow......Page 1011.djvu
3 Laboratory Generators of Gravitational Waves......Page 1012.djvu
4 Astrophysical Sources of Gravitational Waves General Discussion......Page 1013.djvu
5 Gravitational Collapse, Black Holes, Supernovae, and Pulsars as Sources......Page 1014.djvu
6 Binary Stars as Sources......Page 1019.djvu
7 Formulas for Radiation from Nearly Newtonian Slow-Motion Sources......Page 1022.djvu
8 Radiation Reaction in Slow-Motion Sources......Page 1026.djvu
9 Foundations for Derivation of Radiation Formulas......Page 1028.djvu
10 Evaluation of the Radiation Field In the Slow-Motion Approximation......Page 1029.djvu
11 Derivation of the Radiation-Reaction Potential......Page 1034.djvu
1 Coordinate Systems and Impinging Waves......Page 1037.djvu
2 Accelerations in Mechanical Detectors......Page 1039.djvu
3 Types of Mechanical Detectors......Page 1045.djvu
4 Vibrating, Mechanical Detectors Introductory Remarks......Page 1052.djvu
5 Idealized Wave-Dominated Detector, Excited by Steady Flux of Monochromatic Waves......Page 1055.djvu
6 Idealized, Wave-Dominated Detector, Excited by Arbitrary Flux of Radiation......Page 1059.djvu
7 General Wave-Dominated Detector, Excited by Arbitrary Flux of Radiation......Page 1061.djvu
8 Noisy Detectors......Page 1069.djvu
10 Looking Toward the Future......Page 1073.djvu
Part IX. EXPERIMENTAL TESTS OF GENERAL RELATIVITY......Page 1078.djvu
1 Testing iS Easier in the Solar System than In Remote Space......Page 1080.djvu
2 Theoretical Frameworks for Analyzing Tests of General Relativity......Page 1081.djvu
3 Tests of the Principle of the Uniqueness of Free Fall. Eotvos-Dicke Experiment......Page 1083.djvu
4 Tests for the Existence of a Metric Governing Length and Time Measurements......Page 1087.djvu
5 Tests of Geodesic Motion Gravitational Redshift Experiments......Page 1088.djvu
6 Tests of the Equivalence Principle......Page 1093.djvu
7 Tests for the Existence of Unknown Long-Range Fields......Page 1096.djvu
1 Other Theories......Page 1099.djvu
2 Metric Theories of Gravity......Page 1100.djvu
3 Post-Newtonian Limit and PPN Formalism......Page 1101.djvu
4 PPN Coordinate System......Page 1106.djvu
5 Description of the Matter in the Solar System......Page 1107.djvu
6 Nature of the Post-Newtonian Expansion......Page 1108.djvu
7 Newtonian Approximation......Page 1110.djvu
8 PPN Metric Coefficients......Page 1113.djvu
9 Velocity of PPN Coordinates Relative to \"Universal Rest Frame\"......Page 1116.djvu
10 PPN Stress-Energy Tensor......Page 1119.djvu
11 PPN Equations of Motion......Page 1120.djvu
13 Summary of PPN Formalism......Page 1124.djvu
1 Many Experiments Open to Distinguish General Relativity from Proposed Metric Theories of Gravity......Page 1129.djvu
2 The Use of Light Rays and Radio Waves to Test Gravity......Page 1132.djvu
3 \"Light\" Deflection......Page 1134.djvu
4 Time-Delay In Radar PropagatIon......Page 1136.djvu
5 Perihelion Shift and Periodic Perturbations In Geodesic Orbits......Page 1143.djvu
6 Three-Body Effects in the Lunar Orbit......Page 1149.djvu
7 The Dragging of Inertial Frames......Page 1150.djvu
8 Is the Gravitational Constant Constant?......Page 1154.djvu
9 Do Planets and the Sun Move on Geodesics?......Page 1159.djvu
10 Summary of Experimental Tests of General Relativity......Page 1164.djvu
Part X. FRONTIERS......Page 1166.djvu
1 Reflections, Rotations, and the Combinatlon of Rotations......Page 1168.djvu
2 Infinitesimal Rotations......Page 1173.djvu
3 Lorentz Transformation via Spinor Algebra......Page 1175.djvu
4 Thomas Precession via Spinor Algebra......Page 1178.djvu
5 Spinors......Page 1181.djvu
6 Correspondence Between Vectors and Spinors......Page 1183.djvu
7 Spinor Algebra......Page 1184.djvu
8 Spin Space and Its Basis Spinors......Page 1189.djvu
9 Spinor Viewed as Flagpole Plus Flag Plus Orientatlon-Entanglement Relation......Page 1190.djvu
10 Appearance of the Night Sky An Application of Spinors......Page 1193.djvu
11 Spinors as a Powerful Tool in Gravitation Theory......Page 1197.djvu
2 Regge Calculus In Brief......Page 1199.djvu
3 Simplexes and Deficit Angles......Page 1200.djvu
4 Skeleton Form of Field Equations......Page 1202.djvu
5 The Choice of Lattice Structure......Page 1206.djvu
6 The Choice of Edge Lengths......Page 1210.djvu
7 Past Applications of Regge Calculus......Page 1211.djvu
8 The Future of Regge Calculus......Page 1212.djvu
1 Space, Superspace, and Spacetime Distinguished......Page 1213.djvu
2 The Dynamics of Geometry Described in the Language of the Superspace of the ^(3)G\'s......Page 1217.djvu
3 The Einstein-Hamilton-Jacobi Equation......Page 1218.djvu
4 Fluctuations in Geometry......Page 1223.djvu
1 Gravitational Collapse as the Greatest Crisis in PhysIcs of All Time......Page 1229.djvu
2 Assessment of the Theory that Predicts Collapse......Page 1231.djvu
3 Vacuum Fluctuations: Their Prevalence and Final Dominance......Page 1235.djvu
4 Not Geometry, but Pregeometry, as the Magic Building Material......Page 1236.djvu
5 Pregeometry as the Calculus of Propositions......Page 1241.djvu
6 The Black Box: The Reprocessing of the Universe......Page 1242.djvu
Bibliography and Index of Names......Page 1254.djvu
Subject Index......Page 1288.djvu
Endpapers......Page 1313.djvu