Preface Introduction 1 Vector and tensor fields 1.0 Introduction 1.1 Coordinate systems in Euclidean space 1.2 Suffix notation 1.3 Tangents and gradients 1.4 Coordinate transformations in Euclidean space 1.5 Tensor fields in Euclidean space 1.6 Surfaces in Euclidean space 1.7 Manifolds 1.8 Tensor fields on manifolds 1.9 Metric properties 1.10 What and where are the bases Problems 1 2 The spacetime of general relativity and paths of particles 2.0 Introduction 2.1 Geodesics 2.2 Parallel vectors along a curve 2.3 Absolute and covariant differentiation 2.4 Geodesic coordinates 2.5 The spacetime of general relativity 2.6 Newton''s laws of motion 2.7 Gravitational potential and the geodesic 2.8 Newton''s law of universal gravitation 2.9 A rotating reference system Problems 2 3 Field equations and curvature 3.0 Introduction 3.1 The stress tensor and fluid motion 3.2 The curvature tensor and related tensors 3.3 Curvature and parallel transport 3.4 Geodesic deviation 3.5 Einstein''s field equations 3.6 Einstein''s equation compared with Poisson''s equation 3.7 The Schwarzschild solution Problems 3 Physics in the vicinity of a massive object 4.0 Introduction 4.1 Length and time 4.2 Radar sounding 4.3 Spectral shift 4.4 General particle motion including photons 4.5 Perihelion advance 4.6 Bending of light 4.7 Geodesic effect 4.8 Black holes 4.9 Other coordinate systems Problems 4 5 Gravitational radiation 5.0 Introduction 5.1 What wiggles 5.2 Two polarizations 5.3 Simple generation and detection Problems 5 6 Elements of cosmology 6.0 Introduction 6.1 Robertson-Walker line element 6.2 Field equations 6.3 The Friedmann models 6.4 Comment on Einstein''s models 6.5 Newtonian dust Problems 6 A Special relativity review A.0 Introduction A.1 Lorentz transformations A.2 Relativistic addition of velocities A.3 Simultaneity A.4 Time dilation, length contraction A.5 Spacetime diagrams A.6 Some standard 4-vectors A.7 Doppler effect A.8 Electromagnetism Problems A B The Chinese connection B.0 Background B.1 Lanchester''s transporter on a plane B.2 Lanchester''s transporter on a surface B.3 A trip at constant latitude References Index
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