http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
General relativity for the gifted amateur
Using numerous worked examples, diagrams and careful physically motivated explanations this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that general relativity provides and which all physicists should have the opportunity to experience.
Cover -- Title Page -- Copyright Page -- Preface -- Contents -- 0 Overture -- 0.1 What is relativity? -- 0.2 What is general relativity? -- 0.3 What is a metric? -- 0.4 What are we building on? -- 0.5 Who is this book for? -- 0.6 Units in this book -- Exercises -- I Geometry and mechanics in at spacetime -- 1 Special relativity -- 1.1 A common sense start -- 1.2 The speed of light -- 1.3 Light cones and the Lorentz transformation -- 1.4 Paths through spacetime -- 1.5 Experiments -- Chapter summary -- Exercises -- 2 Vectors in at spacetime -- 2.1 Vectors -- 2.2 Coordinate transformations
2.3 Examples of vectors -- 2.4 Principle of least action -- Chapter summary -- Exercises -- 3 Coordinates -- 3.1 Coordinates in Euclidean space -- 3.2 Farewell to the position vector -- 3.3 Non-Euclidean space -- Chapter summary -- Exercises -- 4 Linear slot machines -- 4.1 Dot products and down vectors -- 4.2 Vectors and 1-forms -- 4.3 Transformations -- 4.4 Tensors -- 4.5 Energy-momentum tensor -- Chapter summary -- Exercises -- 5 The metric -- 5.1 Metrics in general -- 5.2 Meet some metrics -- 5.3 Light and light cones -- 5.4 Lengths, areas, volumes -- Chapter summary -- Exercises
II Curvature and general relativity -- 6 Finding a theory of gravitation -- 6.1 Free fall and the equivalence principle -- relativity? -- 6.2 Why -- 6.3 A di erential equation to describe gravity -- 6.4 Local atness -- 6.5 Time dilation in a gravitational eld -- Chapter summary -- Exercises -- 7 Parallel lines and the covariant derivative -- 7.1 Parallelism -- 7.2 Derivatives and connections -- 7.3 The covariant derivative -- 7.4 Parametrized paths -- 7.5 Enter the metric -- Chapter summary -- Exercises -- 8 Free fall and geodesics -- 8.1 Extremal intervals -- 8.2 A geodesic equation
8.3 Inertial forces -- 8.4 Geodesics for photons -- Chapter summary -- Exercises -- 9 Geodesic equations and connection coefficients -- 9.1 Finding connection coe cients -- 9.2 The geodesic equation from the action -- Chapter summary -- Exercises -- 10 Making measurements in relativity -- 10.1 Observers and their observations -- 10.2 Coordinate and non-coordinate bases -- 10.3 The orthonormal frame -- 10.4 Freely falling frames -- Chapter summary -- Exercises -- 11 Riemann curvature and the Ricci tensor -- 11.1 What is curvature? -- 11.2 Tidal forces -- 11.3 Riemann curvature
11.4 Symmetries of the Riemann tensor -- 11.5 The Ricci tensor and Ricci scalar -- 11.6 Example computations -- 11.7 Geodesic deviation revisited -- Chapter summary -- Exercises -- 12 The energy-momentum tensor -- 12.1 Another look at the energy-momentum tensor -- 12.2 Example energy-momentum tensors -- 12.3 Classical particles -- 12.4 Conservation laws -- Chapter summary -- Exercises -- 13 The gravitational field equations -- 13.1 Geometry: a recap of the key ingredients -- 13.2 Physics: the key ingredients -- 13.3 An incorrect guess -- 13.4 Einstein's eld equation -- Chapter summary