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Basics of geometry and relativity | |
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Two dimensional geometry | |
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Inertial and gravitational masses | |
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Relativity | |
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Relativistic dynamics | |
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Relativistic point particle | |
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Current and charge densities | |
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Maxwell's equations in the presence of sources | |
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Motion of a charged particle in EM field | |
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Energy-momentum tensor | |
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Angular momentum | |
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Principle of general covariance | |
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Principle of equivalence | |
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Principle of general covariance | |
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Tensor densities | |
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Affine connection and covariant derivative | |
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Parallel transport of a vector | |
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Christoffel symbol | |
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Covariant derivative of contravariant tensors | |
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Metric compatibility | |
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Covariant derivative of covariant and mixed tensors | |
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Electromagnetic analogy | |
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Gradient, divergence and curl | |
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Geodesic equation | |
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Covariant differentiation along a curve | |
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Curvature from derivatives | |
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Parallel transport along a closed curve | |
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Geodesic equation | |
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Derivation of geodesic equation from a Lagrangian | |
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Applications of the geodesic equation | |
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Geodesic as representing gravitational effect | |
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Rotating coordinate system and the Coriolis force | |
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Gravitational red shift | |
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Twin paradox and general covariance | |
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Other equations in the presence of gravitation | |
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Curvature tensor and Einstein's equation | |
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Curvilinear coordinates versus gravitational field | |
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Definition of an inertial coordinate frame | |
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Geodesic deviation | |
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Properties of the curvature tensor | |
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Einstein's equation | |
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Cosmological constant | |
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Initial value problem | |
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Einstein's equation from an action | |
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Schwarzschild solution | |
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Line element | |
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Connection | |
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Solution of the Einstein equation | |
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Properties of the Schwarzschild solution | |
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Isotropic coordinates | |
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Tests of general relativity | |
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Radar echo experiment | |
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Motion of a particle in a Schwarzschild background | |
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Vertical free fall | |
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Circular orbit | |
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Motion of light rays in a Schwarzschild background | |
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Perihelion advance of Mercury | |
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Black holes | |
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Singularities of the metric | |
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Singularities of the Schwarzschild metric | |
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Black holes | |
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Cosmological models and the big bang theory | |
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Homogeneity and isotropy | |
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Different models of the universe | |
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Close universe | |
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Flat universe | |
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Open universe | |
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Hubble's law | |
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Evolution equation | |
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k = 1 | |
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k = 0 | |
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k = -1 | |
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Big bang theory and blackbody radiation | |
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Index | |