Gravitation and cosmology : principles and applications of the general theory of relativity

Main subject categories: • General Relativity • Gravitation • CosmologyGravitation and Cosmology: Principles and Applications of the General Theory of Relativity offers a Nobel laureate's perspectives on the wealth of data technological developments have brought to expand upon Einstein's theory. Unique in basing relativity on the Principle of Equivalence of Gravitation and Inertia over Riemannian geometry, this book explores relativity experiments and observational cosmology to provide a sound foundation upon which analyses can be made. Covering special and general relativity, tensor analysis, gravitation, curvature, and more, this book provides an engaging, insightful introduction to the forces that shape the universe.(OCR, with TOC bookmarks) CONTENTS PART ONE PRELIMINARIES 1 HISTORICAL INTRODUCTION 1.1 History of Non-Euclidean Geometry 1.2 History of the Theory of Gravitation 1.3 History of the Principle of Relativity Bibliography References 2 SPECIAL RELATIVITY 2.1 Lorentz Transformations 2.2 Time Dilation 2.3 Particle Dynamics 2.4 Energy and Momentum 2.5 Vectors and Tensors 2.6 Currents and Densities 2.7 Electrodynamics 2.8 Energy-Momentum Tensor 2.9 Spin 2.10 Relativistic Hydrodynamics 2.11 Relativistic Imperfect Fluids* 2.12 Representations of the Lorentz Group* 2.13 Temporal Order and Antiparticles* Bibliography References PART TWO THE GENERAL THEORY OF RELATIVITY 3 THE PRINCIPLE OF EQUIVALENCE 3.1 Statement of the Principle 3.2 Gravitational Forces 3.3 Relation between g_μν and Γ_μν^λ 3.4 The Newtonian Limit 3.5 Time Dilation 3.6 Signs of the Times 3.7 Relativity and Anisotropy of Inertia Bibliography References 4 TENSOR ANALYSIS 4.1 The Principle of General Covariance 4.2 Vectors and Tensors 4.3 Tensor Algebra 4.4 Tensor Densities 4.5 Transformation of the Affine Connection 4.6 Covariant Differentiation 4.7 Gradient, Curl, and Divergence 4.8 Vector Analysis in Orthogonal Coordinates* 4.9 Covariant Differentiation Along a Curve 4.10 The Electromagnetic Analogy* 4.11 p-Forms and Exterior Derivatives* References 5 EFFECTS OF GRAVITATION 5.1 Particle Mechanics 5.2 Electrodynamics 5.3 Energy-Momentum Tensor 5.4 Hydrodynamics and Hydrostatics References 6 CURVATURE 6.1 Definition of the Curvature Tensor 6.2 Uniqueness of the Curvature Tensor 6.3 Round Trips by Parallel Transport 6.4 Gravitation versus Curvilinear Coordinates 6.5 Commutation of Covariant Derivatives 6.6 Algebraic Properties of R_λμνκ 6.7 Description of Curvature in N Dimensions* 6.8 The Bianchi Identities 6.9 The Geometric Analogy* 6.10 Geodesic Deviation* Bibliography References 7 EINSTEIN'S FIELD EQUATIONS 7.1 Derivation of the Field Equations 7.2 Another Derivation* 7.3 The Brans-Dicke Theory 7.4 Coordinate Conditions 7.5 The Cauchy Problem 7.6 Energy, Momentum, and Angular Momentum of Gravitation Bibliography References PART THREE APPLICATIONS OF GENERAL RELATIVITY 8 CLASSIC TESTS OF EINSTEIN'S THEORY 8.1 The General Static Isotropic Metric 8.2 The Schwarzschild Solution 8.3 Other Metrics 8.4 General Equations of Motion 8.5 Unbound Orbits: Deflection of Light by the Sun 8.6 Bound Orbits: Precession of Perihelia 8.7 Radar Echo Delay 8.8 The Schwarzschild Singularity* Bibliography References 9 POST-NEWTONIAN CELESTIAL MECHANICS 9.1 The Post-Newtonian Approximation 9.2 Particle and Photon Dynamics 9.3 The Energy-Momentum Tensor 9.4 Multipole Fields 9.5 Precession of Perihelia 9.6 Precession of Orbiting Gyroscopes 9.7 Spin Precession and Mach's Principle* 9.8 Post-Newtonian Hydrodynamics* 9.9 Approximate Solutions to the Brans-Dicke Theory Bibliography References 10 GRAVITATIONAL RADIATION 10.1 The Weak-Field Approximation 10.2 Plane Waves 10.3 Energy and Momentum of Plane Waves 10.4 Generation of Gravitational Waves 10.5 Quadrupole Radiation 10.6 Scattering and Absorption of Gravitational Radiation 10.7 Detection of Gravitational Radiation 10.8 Quantum Theory of Gravitation* 10.9 Gravitational Disturbances in Gravitational Fields* Bibliography References 11 STELLAR EQUILIBRIUM AND COLLAPSE 11.1 Differential Equations for Stellar Structure 11.2 Stability 11.3 Newtonian Stars: Polytropes and White Dwarfs 11.4 Neutron Stars 11.5 Supermassive Stars 11.6 Stars of Uniform Density 11.7 Time-Dependent Spherically Symmetric Fields 11.8 Comoving Coordinates 11.9 Gravitational Collapse Bibliography References PART FOUR FORMAL DEVELOPMENTS 12 THE ACTION PRINCIPLE 12.1 The Matter Action: An Example 12.2 General Definition of T^μν 12.3 General Covariance and Energy-Momentum Conservation 12.4 The Gravitational Action 12.5 The Tetrad Formalism* References 13 SYMMETRIC SPACES 13.1 Killing Vectors 13.2 Maximally Symmetric Spaces: Uniqueness 13.3 Maximally Symmetric Spaces: Construction 13.4 Tensors in a Maximally Symmetric Space 13.5 Spaces with Maximally Symmetric Subspaces Bibliography References PART FIVE COSMOLOGY 14 COSMOGRAPHY 14.1 The Cosmological Principle 14.2 The Robertson-Walker Metric 14.3 The Red Shift 14.4 Measures of Distance 14.5 The Cosmic Distance Ladder 14.6 The Red-Shift Versus Distance Relation 14.7 Number Counts 14.8 The Steady State Cosmology Bibliography References 15 COSMOLOGY: THE STANDARD MODEL 15.1 Einstein's Equations 15.2 Density and Pressure of the Present Universe 15.3 The Matter-Dominated Era 15.4 Intergalactic Emission and Absorption Processes 15.5 The Cosmic Microwave Radiation Background 15.6 Thermal History of the Early Universe 15.7 Helium Synthesis 15.8 The Formation of Galaxies 15.9 Newtonian Theory of Small Fluctuations 15.10 General-Relativistic Theory of Small Fluctuations 15.11 The Very Early Universe Bibliography References 16 COSMOLOGY: OTHER MODELS 16.1 Naive Models: The Olbers Paradox 16.2 Models with a Cosmological Constant 16.3 The Steady State Model Revisited 16.4 Models with a Varying Constant of Gravitation Bibliography References APPENDIX Some Useful Numbers INDEX Weinberg's 1972 Work, In His Description, Had Two Purposes. The First Was Practical To Bring Together And Assess The Wealth Of Data Provided Over The Previous Decade While Realizing That Newer Data Would Come In Even As The Book Was Being Printed. He Hoped The Comprehensive Picture Would Prepare The Reader And Himself To That New Data As It Emerged. The Second Was To Produce A Textbook About General Relativity In Which Geometric Ideas Were Not Given A Starring Role For (in His Words) Too Great An Emphasis On Geometry Can Only Obscure The Deep Connections Between Gravitation And The Rest Of Physics. Part One: Preliminaries -- Part Two: The General Theory Of Relativity -- Part Three: Applications Of General Relativity -- Part Four: Formal Developments -- Part Five: Cosmology -- Appendix -- Some Useful Numbers -- Index. Includes Bibliographical References And Index. A leading physicist delves into relativity and experimental applications Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity offers a Nobel laureate's perspectives on the wealth of data technological developments have brought to expand upon Einstein's theory. Unique in basing relativity on the Principle of Equivalence of Gravitation and Inertia over Riemannian geometry, this book explores relativity experiments and observational cosmology to provide a sound foundation upon which analyses can be made. Covering special and general relativity, tensor analysis, gravitation, curvature, and more, this book provides an engaging, insightful introduction to the forces that shape the universe.