THE THEORY OF THE RELATIVITY OF MOTION
CONTENTS CHAPTER 1 ?RELATIVITY: A THEORY OF SPACE, TIME, AND GRAVITY THE PRINCIPLE OF RELATIVITY THE LAW OF INERTIA: FOUNDATION OF SPECIAL RELATIVITY SPACE, TIME, AND SPACETIME SPACETIME DIAGRAMS RELATIVITY OF CAUSALITY: SPACELIKE AND TIMELIKE SEGUE TO GENERAL RELATIVITY: NONINERTIAL FRAMES GENERAL RELATIVITY: A THEORY OF GRAVITATION HASTA LA VISTA, GRAVITY CHAPTER 2 ?BASIC SPECIAL RELATIVITY COMPARISON OF TIME INTERVALS: THE BONDI K-FACTOR TIME DILATION VELOCITY ADDITION LORENTZ TRANSFORMATION LENGTH CONTRACTION FOUNDATIONAL EXPERIMENTS CHAPTER 3 ?LORENTZ TRANSFORMATION, I FRAMES IN STANDARD CONFIGURATION FRAMES NOT IN STANDARD CONFIGURATION TRANSFORMATION OF VELOCITY AND ACCELERATION RELATIVISTIC ABERRATION AND DOPPLER EFFECT CHAPTER 4 ?GEOMETRY OF LORENTZ INVARIANCE LORENTZ TRANSFORMATIONS AS SPACETIME ROTATIONS KINEMATIC EFFECTS FROM THE INVARIANT HYPERBOLA CLASSIFICATION OF LORENTZ TRANSFORMATIONS SPACETIME GEOMETRY AND CAUSALITY CHAPTER 5 ?TENSORS ON ?AT SPACES TRANSFORMATION PROPERTIES TENSOR DENSITIES, INVARIANT VOLUME ELEMENT DERIVATIVES OF TENSORS AND THE FOUR-WAVEVECTOR INTERLUDE: DRAW A LINE HERE TENSORS AS MULTILINEAR MAPPINGS METRIC TENSOR REVISITED SYMMETRY OPERATIONS ON TENSORS LEVI-CIVITA TENSOR AND DETERMINANTS PSEUDOTENSORS 510 TOTALLY ANTISYMMETRIC TENSORS 511 INTEGRATION ON MINKOWSKI SPACE 512 THE GHOST OF TENSORS YET TO COME CHAPTER 6 ?LORENTZ TRANSFORMATION, II DECOMPOSITION INTO ROTATIONS AND BOOSTS INFINITESIMAL LORENTZ TRANSFORMATION SPINOR REPRESENTATION OF LORENTZ TRANSFORMATIONS THOMAS-WIGNER ROTATION CHAPTER 7 ?PARTICLE DYNAMICS PROPER TIME, FOUR-VELOCITY, AND FOUR-ACCELERATION THE ENERGY-MOMENTUM FOUR-VECTOR ACTION PRINCIPLE FOR PARTICLES KEPLER PROBLEM IN SPECIAL RELATIVITY COVARIANT EULER-LAGRANGE EQUATION PARTICLE CONSERVATION LAWS ENERGY-MOMENTUM CONSERVATION CHAPTER 8 ?COVARIANT ELECTRODYNAMICS ELECTROMAGNETISM IN SPACE AND TIME SOURCES IN SPACETIME: THE FOUR-CURRENT CONSERVATION IN SPACETIME: SPACELIKE HYPERSURFACES THE FOUR-POTENTIAL MAXWELL EQUATIONS IN COVARIANT FORM: FIELD TENSOR LORENTZ TRANSFORMATION OF E AND B FIELDS LORENTZ FORCE AS A RELATIVISTIC EFFECT INVARIANTS OF THE ELECTROMAGNETIC FIELD ACTION PRINCIPLE FOR CHARGED PARTICLES 810 GAUGE INVARIANCE AND CHARGE CONSERVATION CHAPTER 9 ?ENERGY-MOMENTUM OF ?ELDS SYMMETRIES AND CONSERVATION LAWS SPACETIME HOMOGENEITY: ENERGY-MOMENTUM TENSOR SPACETIME ISOTROPY: ANGULAR MOMENTUM TENSOR SYMMETRIC ENERGY-MOMENTUM TENSOR THE ELECTROMAGNETIC FIELD CHAPTER 10 ?RELATIVISTIC HYDRODYNAMICS 101 NONRELATIVISTIC HYDRODYNAMICS 102 ENERGY-MOMENTUM TENSOR FOR PERFECT FLUIDS 103 ENERGY-MOMENTUM CONSERVATION 104 PARTICLE NUMBER CONSERVATION 105 COVARIANT EQUATION OF MOTION 106 LAGRANGIAN DENSITY CHAPTER 11 ?EQUIVALENCE OF LOCAL GRAVITY AND ACCELERATION 111 THE E ¨OTV ¨OS EXPERIMENT 112 THE EQUIVALENCE PRINCIPLE 113 TIDAL FORCES AND REFERENCE FRAMES 114 WEAK AND STRONG EQUIVALENCE PRINCIPLES 115 SPACETIME IS GLOBALLY CURVED, LOCALLY FLAT 116 ENERGY COUPLES TO GRAVITY 117 GRAVITY AFFECTS TIME CHAPTER 12 ?ACCELERATION IN SPECIAL RELATIVITY 121 LINEAR ACCELERATION 122 TWIN PARADOX 123 ROTATING REFERENCE FRAME 124 THE SAGNAC EFFECT 125 RELATIVISTIC DESCRIPTION OF SPIN 126 COVARIANT SPIN DYNAMICS CHAPTER 13 ?TENSORS ON MANIFOLDS 131 MANIFOLDS 132 VECTOR AND TENSOR FIELDS 133 INTEGRAL CURVES, CONGRUENCES, AND FLOWS 134 MAPPINGS OF TENSORS 135 THE LIE DERIVATIVE 136 SUBMANIFOLDS, EMBEDDINGS, AND HYPERSURFACES 137 DIFFERENTIAL FORMS AND EXTERIOR DIFFERENTIATION 138 INTEGRATION ON MANIFOLDS CHAPTER 14 ?DIFFERENTIAL GEOMETRY 141 COVARIANT DIFFERENTIATION 142 WHAT DO THE CONNECTION COEFFICIENTS TELL US? 143 PARALLEL TRANSPORT AND GEODESIC CURVES 144 THE RIEMANN TENSOR 145 THE RICCI TENSOR AND SCALAR FIELD 146 THE EINSTEIN TENSOR 147 ISOMETRIES, KILLING VECTORS, AND CONSERVATION LAWS 148 MAXIMALLY SYMMETRIC SPACES CHAPTER 15 ?GENERAL RELATIVITY 151 INTRODUCTION 152 WEAK, STATIC GRAVITY 153 THE EINSTEIN FIELD EQUATION 154 LAGRANGIAN FORMULATION 155 DUST CHAPTER 16 ?THE SCHWARZSCHILD METRIC STATIC, SPHERICALLY SYMMETRIC SPACETIME METRICS RICCI TENSOR FOR THE SCHWARZSCHILD METRIC THE VACUUM SOLUTION BIRKHOFF’S THEOREM SPATIAL GEOMETRY OF THE SCHWARZSCHILD METRIC CHAPTER 17 ?PHYSICAL EFFECTS OF SCHWARZSCHILD SPACETIME GEODESICS IN SCHWARZSCHILD SPACETIME PARTICLE TRAJECTORIES RADIAL NULL GEODESICS: KRUSKAL COORDINATES GRAVITATIONAL DEFLECTION OF LIGHT APSIDAL PRECESSION GRAVITATIONAL TIME DELAY PARAMETERIZED POST-NEWTONIAN FRAMEWORK THE GLOBAL POSITIONING SYSTEM SPIN PRECESSION I: GEODETIC EFFECT 1710 WEIGHT OF AN AT-REST OBSERVER CHAPTER 18 ?LINEARIZED GRAVITY LINEARIZED FIELD EQUATION STATIC SOURCE FAR FROM A SLOWLY VARYING SOURCE GRAVITOMAGNETISM: STATIONARY SOURCES FRAME DRAGGING SLOWLY ROTATING SOURCE SPIN PRECESSION II: THE LENSE-THIRRING EFFECT GRAVITATIONAL WAVES ENERGY-MOMENTUM OF GRAVITATION CHAPTER 19 ?RELATIVISTIC COSMOLOGY THE COSMOLOGICAL PRINCIPLE A COORDINATE SYSTEM FOR COSMOLOGY SPACES OF CONSTANT CURVATURE FRIEDMANN-ROBERTSON-WALKER SPACETIME SPATIAL GEOMETRIES THE FRIEDMANN EQUATIONS NEWTONIAN COSMOLOGY COSMOLOGICAL REDSHIFT THE EINSTEIN UNIVERSE 1910 THE DE SITTER UNIVERSE 1911 DARK ENERGY 1912 THE FRIEDMANN EVOLUTION EQUATION