RELATIVITY, GRAVITATION AND COSMOLOGY: A BASIC INTRODUCTION

By WILLIAM DAVIS

CONTENTS PARTI RELATIVITY METRIC DESCRIPTION OF SPACETIME INTRODUCTION AND OVERVIEW RELATIVITY AS A COORDINATE SYMMETRY FROM NEWTONIAN RELATIVITY TO AETHER EINSTEINIAN RELATIVITY COORDINATE SYMMETRY TRANSFORMATIONS NEW KINEMATICS AND DYNAMICS GR AS A GRAVITATIONAL ?ELD THEORY EINSTEIN’S MOTIVATIONS FOR THE GENERAL THEORY GEOMETRY AS GRAVITY MATHEMATICAL LANGUAGE OF RELATIVITY GR IS THE FRAMEWORK FOR COSMOLOGY REVIEW QUESTIONS SPECIAL RELATIVITY AND THE ?AT SPACETIME COORDINATE SYMMETRIES ROTATIONAL SYMMETRY NEWTONIAN PHYSICS AND GALILEAN SYMMETRY ELECTRODYNAMICS AND LORENTZ SYMMETRY VELOCITY ADDITION RULE AMENDED THE NEW KINEMATICS OF SPACE AND TIME RELATIVITY OF SPATIAL EQUILOCALITY RELATIVITY OF SIMULTANEITY—THE NEW KINEMATICS THE INVARIANT SPACE–TIME INTERVAL GEOMETRIC FORMULATION OF SR GENERAL COORDINATES AND THE METRIC TENSOR DERIVATION OF LORENTZ TRANSFORMATION THE SPACETIME DIAGRAM TIME-DILATION AND LENGTH CONTRACTION PROBLEMS THE PRINCIPLE OF EQUIVALENCE NEWTONIAN GRAVITATION POTENTIAL—A REVIEW EP INTRODUCED INERTIAL MASS VS GRAVITATIONAL MASS EP AND ITS SIGNI?CANCE IMPLICATIONS OF THE STRONG EP GRAVITATIONAL REDSHIFT AND TIME DILATION LIGHT RAY DE?ECTION CALCULATED ENERGY CONSIDERATIONS OF A GRAVITATING LIGHT PULSE EINSTEIN’S INFERENCE OF A CURVED SPACETIME METRIC DESCRIPTION OF A CURVED SPACE GAUSSIAN COORDINATES METRIC TENSOR GEODESIC AS THE SHORTEST CURVE LOCAL EUCLIDEAN COORDINATES CURVATURE GAUSSIAN CURVATURE SPACES WITH CONSTANT CURVATURE CURVATURE MEASURES DEVIATION FROM EUCLIDEAN RELATIONS GR AS A GEOMETRIC THEORY OF GRAVITY - I EP PHYSICS AND A WARPED SPACETIME CURVED SPACETIME AS GRAVITATIONAL ?ELD GEODESIC EQUATION AS GR EQUATION OF MOTION THE NEWTONIAN LIMIT GRAVITATIONAL REDSHIFT REVISITED THE CURVATURE OF SPACETIME TIDAL FORCE AS THE CURVATURE OF SPACETIME THE GR ?ELD EQUATION DESCRIBED SPACETIME OUTSIDE A SPHERICAL STAR DESCRIPTION OF SCHWARZSCHILD SPACETIME SPHERICALLY SYMMETRIC METRIC TENSOR SCHWARZSCHILD GEOMETRY GRAVITATIONAL LENSING LIGHT RAY DE?ECTION REVISITED THE LENS EQUATION PRECESSION OF MERCURY’S PERIHELION BLACK HOLES SINGULARITIES OF THE SCHWARZSCHILD METRIC TIME MEASUREMENTS IN THE SCHWARZSCHILD SPACETIME LIGHTCONES OF THE SCHWARZSCHILD BLACK HOLE ORBIT OF AN OBJECT AROUND A BLACK HOLE PHYSICAL REALITY OF BLACK HOLES PARTII COSMOLOGY THE HOMOGENEOUS AND ISOTROPIC UNIVERSE THE COSMOS OBSERVED MATTER DISTRIBUTION ON THE COSMIC DISTANCE SCALE COSMOLOGICAL REDSHIFT: HUBBLE’S LAW AGE OF THE UNIVERSE DARK MATTER AND MASS DENSITY OF THE UNIVERSE THE COSMOLOGICAL PRINCIPLE THE ROBERTSON–WALKER METRIC PROPER DISTANCE IN THE RW GEOMETRY REDSHIFT AND LUMINOSITY DISTANCE THE EXPANDING UNIVERSE AND THERMAL RELICS FRIEDMANN EQUATIONS THE QUASI-NEWTONIAN INTERPRETATION TIME EVOLUTION OF MODEL UNIVERSES BIG BANG COSMOLOGY SCALE-DEPENDENCE OF RADIATION TEMPERATURE DIFFERENT THERMAL EQUILIBRIUM STAGES PRIMORDIAL NUCLEOSYNTHESIS PHOTON DECOUPLING AND THE CMB UNIVERSE BECAME TRANSPARENT TO PHOTONS THE DISCOVERY OF CMB RADIATION PHOTONS, NEUTRINOS, AND THE RADIATION–MATTER EQUALITY TIME CMB TEMPERATURE ?UCTUATION IN?ATION AND THE ACCELERATING UNIVERSE THE COSMOLOGICAL CONSTANT VACUUM-ENERGY AS SOURCE OF GRAVITATIONAL REPULSION THE STATIC UNIVERSE THE IN?ATIONARY EPOCH INITIAL CONDITIONS FOR THE STANDARD BIG BANG MODEL THE IN?ATION SCENARIO IN?ATION AND THE CONDITIONS IT LEFT BEHIND CMB ANISOTROPY AND EVIDENCE FOR K = THREEREGIONSOFTHEANGULARPOWERSPECTRUM THE PRIMARY PEAK AND SPATIAL GEOMETRY OF THE UNIVERSE THE ACCELERATING UNIVERSE IN THE PRESENT EPOCH DISTANT SUPERNOVAE AND THE 1998 DISCOVERY TRANSITION FROM DECELERATION TO ACCELERATION THE CONCORDANT PICTURE PARTIII RELATIVITY FULL TENSOR FORMULATION 10 TENSORS IN SPECIAL RELATIVITY 10 1 GENERAL COORDINATE SYSTEMS 10 2 FOUR-VECTORS IN MINKOWSKI SPACETIME 10 3 MANIFESTLY COVARIANT FORMALISM FOR E&M THE ELECTROMAGNETIC ?ELD TENSOR ELECTRIC CHARGE CONSERVATION 10 4 ENERGY–MOMENTUM TENSORS 11 TENSORS IN GENERAL RELATIVITY 11 1 DERIVATIVES IN A CURVED SPACE GENERAL COORDINATE TRANSFORMATIONS COVARIANT DIFFERENTIATION CHRISTOFFEL SYMBOLS AND METRIC TENSOR 11 2 PARALLEL TRANSPORT COMPONENT CHANGES UNDER PARALLEL TRANSPORT THE GEODESIC AS THE STRAIGHTEST POSSIBLE CURVE 11 3 RIEMANNIAN CURVATURE TENSOR THE CURVATURE TENSOR IN AN N-DIMENSIONAL SPACE SYMMETRIES AND CONTRACTIONS OF THE CURVATURE TENSOR 12 GR AS A GEOMETRIC THEORY OF GRAVITY - II 12 1 THE PRINCIPLE OF GENERAL COVARIANCE GEODESIC EQUATION FROM SR EQUATION OF MOTION 12 2 EINSTEIN ?ELD EQUATION FINDING THE RELATIVISTIC GRAVITATIONAL ?ELD EQUATION NEWTONIAN LIMIT OF THE EINSTEIN EQUATION 12 3 THE SCHWARZSCHILD EXTERIOR SOLUTION 12 4 THE EINSTEIN EQUATION FOR COSMOLOGY SOLUTION FOR A HOMOGENEOUS AND ISOTROPIC 3D SPACE EINSTEIN EQUATION WITH A COSMOLOGICAL CONSTANT TERM LINEARIZED THEORY AND GRAVITATIONAL WAVES 13 1 THE LINEARIZED EINSTEIN THEORY THE COORDINATE CHANGE CALLED GAUGE TRANSFORMATION THE WAVE EQUATION IN THE LORENTZ GAUGE 13 2 PLANE WAVES AND THE POLARIZATION TENSOR 13 3 GRAVITATIONAL WAVE DETECTION EFFECT OF GRAVITATIONAL WAVES ON TEST PARTICLES GRAVITATIONAL WAVE INTERFEROMETERS 13 4 EVIDENCE FOR GRAVITATIONAL WAVE ENERGY ?UX IN LINEARIZED GRAVITATIONAL WAVES EMISSION OF GRAVITATIONAL RADIATION