GENERAL RELATIVITY: A GEOMETRIC APPROACH
CONTENTS PART ONE: THE CONCEPT OF SPACETIME INTRODUCTION EXERCISES, EVENTS AND SPACETIME EVENTS, INERTIAL PARTICLES, LIGHT AND NULL CONES, PART TWO: FLAT SPACETIME AND SPECIAL RELATIVITY FLAT SPACETIME DISTANCE, TIME, AND ANGLE, SPEED AND THE DOPPLER EFFECT, THE GEOMETRY OF FLAT SPACETIME SPACETIME VECTORS, THE SPACETIME METRIC, VOLUME AND PARTICLE DENSITY, ENERGY ENERGY AND FOUR-MOMENTUM, THE ENERGY–MOMENTUM TENSOR, GENERAL STATES OF MATTER, PERFECT FLUIDS, ACCELERATION AND THE MAXWELL TENSOR, TENSORS TENSORS AT A POINT, THE ABSTRACT INDEX NOTATION, TENSOR FIELDS CONGRUENCES AND DERIVATIONS, LIE DERIVATIVES, FIELD EQUATIONS CONSERVATION LAWS, MAXWELL’S EQUATIONS, CHARGE, MASS, AND ANGULAR MOMENTUM, PART THREE: CURVED SPACETIME AND GRAVITY CURVED SPACETIME SPACETIME AS A MANIFOLD, THE COVARIANT DERIVATIVE, THE CURVATURE TENSOR, CONSTANT CURVATURE, CURVATURE AND GRAVITY GEODESICS, EINSTEIN’S FIELD EQUATION, GRAVITY AS AN ATTRACTIVE FORCE, NULL CONGRUENCES SURFACE-FORMING NULL CONGRUENCES, TWISTING NULL CONGRUENCES, ASYMPTOTIC FLATNESS AND SYMMETRIES ASYMPTOTICALLY FLAT SPACETIMES, KILLING FIELDS AND STATIONARY SPACETIMES, KERR SPACETIME, ENERGY AND INTRINSIC ANGULAR MOMENTUM, SCHWARZSCHILD GEOMETRIES AND SPACETIMES SCHWARZSCHILD GEOMETRIES, GEODESICS IN A SCHWARZSCHILD SPACETIME, THREE CLASSICAL TESTS OF GENERAL RELATIVITY, SCHWARZSCHILD SPACETIMES, BLACK HOLES AND SINGULARITIES SPHERICAL GRAVITATIONAL COLLAPSE, SINGULARITIES, BLACK HOLES AND HORIZONS, STATIONARY BLACK HOLES AND KERR SPACETIME, THE ERGOSPHERE AND ENERGY EXTRACTION, BLACK-HOLE THERMODYNAMICS, PART FOUR: COSMOLOGY THE SPACETIME OF THE UNIVERSE THE COSMOLOGICAL PRINCIPLE, COSMOLOGICAL RED SHIFTS, THE EVOLUTION OF THE UNIVERSE, HORIZONS, RELATIVISTIC COSMOLOGY FRIEDMANN UNIVERSES, THE COSMOLOGICAL CONSTANT, THE HOT BIG-BANG MODEL, BLACKBODY RADIATION, THE ORIGIN OF THE BACKGROUND RADIATION, A MODEL UNIVERSE, SOLUTIONS AND HINTS TO SELECTED EXERCISES BIBLIOGRAPHY