Lectures on gravitation /
This book is a compilation of the lectures for a one-semester course on gravitation at the University of Rochester. Starting from a simple description of geometry, the topics are systematically developed to the big bang theory with a simple derivation of the cosmic background temperature. Several in...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; Hackensack, NJ :
World Scientific,
©2011.
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| Subjects: | |
| Online Access: |
Full text (Emmanuel users only) |
Table of Contents:
- Basics of geometry and relativity. Two dimensional geometry ; Inertial and gravitational masses ; Relativity
- Relativistic dynamics. Relativistic point particle ; Current and charge densities ; Maxwell's equations in the presence of sources ; Motion of a charged particle in EM field ; Energy-momentum tensor ; Angular momentum
- Principle of general covariance. Principle of equivalence ; Principle of general covariance ; Tensor densities
- Affine connection and covariant derivative. Parallel transport of a vector ; Christoffel symbol ; Covariant derivative of contravariant tensors ; Metric compatibility ; Covariant derivative of covariant and mixed tensors ; Electromagnetic analogy ; Gradient, divergence and curl
- Geodesic equation. Covariant differentiation along a curve ; Curvature from derivatives ; Parallel transport along a closed curve ; Geodesic equation ; Derivation of geodesic equation from a Lagranian
- Applications of the geodesic equation. Geodesic as representing gravitational effect ; Rotating coordinate system and the Coriolis force ; Gravitational red shift ; Twin paradox and general covariance ; Other equations in the presence of gravitation
- Curvature tensor and Einstein's equation. Curvilinear coordinates versus gravitational field ; Definition of an inertial coordinate frame ; Geodesic deviation ; Properties of the curvature tensor ; Einstein's equation ; Cosmological constant ; Initial value problem ; Einstein's equation from an action
- Schwarzschild solution. Line element ; Connection ; Solution of the Einstein equation ; Properties of the Schwarzschild solution ; Isotropic coordinates
- Tests of general relativity. Radar echo experiment ; Motion of a particle in a Schwarzschild background ; Motion of light rays in a Schwarzschild background ; Perihelion advance of Mercury
- Black holes. Singularities of the metric ; Singularities of the Schwarzschild metric ; Black holes
- Comological models and the big bang theory. Homogeneity and isotropy ; Different models of the universe ; Hubble's law ; Evolution equation ; Big bang theory and blackbody radiation.