Relativity and Geometry

Introduction 1(7) Newtonian Principles 8(27) The Task of Natural Philosophy 8(1) Absolute Space 9(2) Absolute Time 11(3) Rigid Frames and Coordinates 14(1) Inertial Frames and Newtonian Relativity 15(5) Newtonian Spacetime 20(11) Gravitation 31(4) Electrodynamics and the Aether 35(13) Nineteenth-Century Views on Electromagnetic Action 35(3) The Relative Motion of the Earth and the Aether 38(10) Einstein's `Electrodynamics of Moving Bodies' 48(40) Motivation 48(2) The Definition of Time in an Inertial Frame 50(4) The Principles of Special Relativity 54(2) The Lorentz Transformation. Einstein's Derivation of 1905 56(10) The Lorentz Transformation. Some Corollaries and Applications 66(5) The Lorentz Transformation. Linearity 71(5) The Lorentz Transformation. Ignatowsky's Approach 76(7) The ``Relativity Theory of Poincare and Lorentz'' 83(5) Minkowski Spacetime 88(42) The Geometry of the Lorentz Group 88(3) Minkowski Spacetime as an Affine Metric Space and as a Riemannian Manifold 91(7) Geometrical Objects 98(9) Concept Mutation at the Birth of Relativistic Dynamics 107(7) A Glance at Spacetime Physics 114(7) The Causal Structure of Minkowski Spacetime 121(9) Einstein's Quest for a Theory of Gravity 130(56) Gravitation and Relativity 130(3) The Principle of Equivalence 133(4) Gravitation and Geometry circa 1912 137(6) Departure from Flatness 143(9) General Covariance and the Einstein-Grossmann Theory 152(10) Einstein's Arguments against General Covariance: 1913-14 162(6) Einstein s Papers of November 1915 168(8) Einstein's Field Equations and the Geodesic Law of Motion 176(10) Gravitational Geometry 186(34) Structures of Spacetime 186(8) Mach's Principle and the Advent of Relativistic Cosmology 194(8) The Friedmann Worlds 202(8) Singularities 210(10) Disputed Questions 220(37) The Concept of Simultaneity 220(10) Geometric Conventionalism 230(17) Remarks on Time and Causality 247(10) Appendix 257(26) A. Differentiable Manifolds 257(6) B. Fibre Bundles 263(2) C. Linear Connections 265(16) 1. Vector-valued Differential Forms 2. The Lie Algebra of a Lie Group 3. Connections in a Principal Fibre Bundle 4. Linear Connections 5. Covariant Differentiation 6. The Torsion and Curvature of a Linear Connection 7. Geodesics 8. Metric Connections in Riemannian Manifolds D. Useful Formulae 281(2) Notes 283(68) References 351(30) Index 381