Upon the completion of the course, the students are expected to have
1) familiarized themselves with using tensors,
2) comprehended the axioms of the theory of general relativity,
3) comprehended the implications and the applications of the theory of general relativity,
4) obtained the ability to solve exercises in general relativity.
Course Content (Syllabus)
Tensor Calculus (Algebraic Operations, Symmetries, Covariant Diferentiation, Connections, Parallel Transport, Geodesics, Curvature Tensor) - Riemann Geometry (Riemannian Spaces, Metric Τensor, Christoffel Symbols, Geodesics, Curvature Tensor, Geodesic Deviation, Weyl Tensor, Algebraic Classification, Lie Derivatives, Isometries, Killing Vectors) - The Gravitational Field (Linearized Field Equations, The Principle of Equivalence, Einstein's Field Equations of General Theory of Relativity) - Physics in the Presence of Gravitation - Solutions to the Einstein Equations (Schwarzschild, Reissner-Nordstrom, Kerr, Kerr-Newman) - Tests and Applications of the General Theory of Relativity (Advance of the Perihelion of a Planet, The Deflection of the Light Rays, Gravitational Red Shift, The Delay of Radar Signals) - Gravitational Collapse, Black Holes (Schwarzschild, Kerr, Kerr-Newman) - Weak Gravitational Fields, Gravitational Waves (Sources, Propagation, Detection.