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.