# INTRODUCTION TO GENERAL RELATIVITY (2nd)

Introduction to General Relativity (Pure & Applied Physics S.)

• INTRODUCTION
• 1. Physics and Geometry
• 2. The Choice of Riemannian Geometry
• CHAPTER 1 TENSOR ALGEBRA
• 1.1 Definition of Scalars, Contravariant Vectors, and Covariant Vectors
• 1.2 Einstein's Summation Convention
• 1.3 Definitions of Tensors
• 1.4 Tensor Algebra
• 1.5 Decomposition of a Tensor into a Sum of Vector Products
• 1.6 Contraction of Indices
• 1.7 The Quotient Theorem
• 1.8 Lowering and Raising of Indices---Associated Tensors
• 1.9 Connection with Vector Calculus in Euclidean Space
• 1.10 Connection between Bilinear Forms and Tensor Calculus
• CHAPTER 2 VECTOR FIELDS IN AFFINE AND RIEMANN SPACE
• 2.1 Vector Transplantation and Affine Connections
• 2.2 Parallel Displacement---Christoffel Symbols
• 2.3 Geodesics in Affine and Riemann Space
• 2.4 Gaussian Coordinates
• CHAPTER 3 TENSOR ANALYSIS
• 3.1 Covariant Differentiation
• 3.2 Applications of Tensor Analysis
• 3.3 Symmetric and Antisymmetric Tensors
• 3.4 Closed and Exact Tensors
• 3.5 Tensor Densities---Dual Tensors
• 3.6 Vector Fields on Curves
• 3.7 Intrinsic Symmetries and Killing Vectors
• CHAPTER 4 TENSORS IN PHYSICS
• 4-1 Maxwell's Equations in Tensor Form
• 4.2 Proper-Time and the Equations of Motion via an Example in Relativistic Mechanics
• 4.3 Gravity as a Metric Phenomenon
• 4.4 The Red Shift
• CHAPTER 5 THE GRAVITATIONAL FIELD EQUATIONS IN FREE SPACE
• 5.1 Criteria for the Field Equations
• 5.2 The Riemann Curvature Tensor
• 5.3 Symmetry Properties of the Riemann Tensor
• 5.4 The Bianchi Identities
• 5.5 Integrability and the Riemann Tensor
• 5.6 Pseudo-Euclidean and Flat Spaces
• 5.8 The Divergenceless Form of the Einstein Field Equations
• 5.9 The Riemann Tensor and Fields of Geodesies
• 5.10 Algebraic Properties of the Riemann Tensor
• CHAPTER 6 THE SCHWARZSCHILD SOLUTION AND ITS CONSEQUENCES: EXPERIMENTAL TESTS OF GENERAL RELATIVITY
• 6.1 The Schwarzschild Solution
• 6.2 The Schwarzschild Solution in Isotropic Coordinates
• 6.3 The General Relativistic Kepler Problem and the Perihelic Shift of Mercury
• 6.4 The Sun's Quadrupole Moment and Perihelic Motion
• 6.5 The Trajectory of a Light Ray in a Schwarzschild Field
• 6.6 Travel Time of Light in a Schwarzschild Field
• 6.7 Null Geodesies and Fermat's Principle
• 6.8 The Schwarzschild Radius, Kruskal Coordinates, and the Black Hole
• CHAPTER 7 THE KERR SOLUTION
• 7.1 Eddington's Form of the Schwarzschild Solution
• 7.2 Einstein's Equations for Degenerate Metrics
• 7.3 The Order Equations
• 7.4 Field Equations for the Stationary Case
• 7.5 The Schwarzschild and Kerr Solutions
• 7.6 Other Coordinates
• 7.7 The Kerr Solution and Rotation
• 7.8 Distinguished Surfaces and the Rotating Black Hole
• 7.9 Effective Potentials and Black Hole Energetics
• CHAPTER 8 THE MATHEMATICAL STRUCTURE OF THE EINSTEIN DIFFERENTIAL SYSTEM; THE PROBLEM OF CAUCHY
• 8.1 Formulation of the Initial-Value Problem
• 8.2 Structure of Einstein's Equations
• 8.8 Separation of the Cauchy Problem into Two Parts
• 8.4 Characteristic Hypersurfaces of the Einstein Equation System
• 8.5 Bicharacteristics of the Einstein System
• 8.6 Uniqueness Problem for the Einstein Equations
• 8.7 The Maximum Principle for the Generalized Laplace Equation
• CHAPTER 9 THE LINEARIZED FIELD EQUATIONS
• 9.1 Linearization of the Field Equations
• 9.2 The Time-independent and Spherically Symmetric Field
• 9.3 The Weyl Solutions to the Linearized Field Equations
• 9.4 Structure of the Linearized Equations
• 9.5 Gravitational Waves
• CHAPTER 10 THE GRAVITATIONAL FIELD EQUATIONS FOR NONEMPTY SPACE
• 10.1 The Energy-Momentum Tensor
• 10.2 Inclusion of Forces in
• 10.3 The Electromagnetic Field and
• 10.4 The Field Equations in Nonempty Space
• 10.5 Classical Limit of the Gravitational Equations
• CHAPTER 11 FURTHER CONSEQUENCES OF THE FIELD EQUATIONS
• 11.1 The Equations of Motion
• 11.2 Conservation Laws in General Relativity: Energy-Momentum of the Gravitational Field
• 11.3 An Alternative Approach to the Conservation Laws: Energy-Momentum of the Schwarzschild Field
• 11.4 Variational Principles in General Relativity Theory: A Lagrangian Density for the Gravitational Field
• 11.5 The Scalar Tensor Variation of Relativity Theory
• CHAPTER 12 DESCRIPTIVE COSMIC ASTRONOMY
• 12.1 Observational Background
• 12.2 The Mathematical Problem in Outline
• 12.3 The Robertson-Walker Metric
• 12.4 Further Properties of the Robertson-Walker Metric
• 12.6 The Red Shift and the Robertson-Walker Metric: Hubble's Law
• 12.6 The Apparent Magnitude-Red Shift Relation
• CHAPTER 13 COSMOLOGICAL MODELS
• 13.1 Einstein's Equations and the Robertson-Walker Metric
• 13.2 Static Models of the Universe
• 13.3 Nonstatic Models of the Universe
• 13.4 The Godel Solution and Mach's Principle
• 13.5 The Steady-State Model of the Universe
• 13.6 Converse of the Apparent Magnitude-Red Shift Problem
• CHAPTER 14 THE ROLE OF RELATIVITY IN STELLAR STRUCTURE AND GRAVITATIONAL COLLAPSE
• 14.1 Relativistic Stellar Structure
• 14.2 A Simple Stellar Model---The Interior Schwarzschild Solution
• 14.8 Stellar Models and Stability
• 14.4 Gravitational Collapse of a Dust Ball
• CHAPTER 15 ELECTROMAGNETISM AND GENERAL RELATIVITY
• 15.1 The Field of a Charged Mass Point
• 15.2 Weyl's Generalization of Riemannian Geometry
• 15.3 Weyl's Theory of Electromagnetism
• 15.4 Some Mathematical Machinery
• 15.5 The Equations of Rainich, Misner, and Wheeler
• INDEX