This class represents an introduction to the theory of general relativity (GR). It starts with an introduction to differential geometry, the language in which GR is written. After that, the Einstein field equations are derived heuristically, and are finally solved in certain contexts, such as spherical symmetry (leading to the Schwarzschild solution), gravity waves and cosmology
Expected learning outcomes
At the end of the course the student is expected to have the following skills: 1. Profound knowledge of differential geometry; 2. Knows the Einstein field equations and their Newtonian limit; 3. Is able to solve the Einstein equations in a context with enough symmetry; 4. Knows the physics of the Schwarzschild solution and the classical tests of GR; 5. Knowledge in modern cosmology.
First half (about 24 hours): Brief summary of special relativity; introduction to differential geometry: Differential manifolds, tangent and cotangent space, tensor analysis, differential forms, (pseudo-)Riemannian manifolds, linear connections, curvature. Second half: Einstein equations, Schwarzschild solution, classical tests of GR, black holes, FRW cosmology, gravitational waves.
Prerequisites for admission
Knowledge of special relativity and analytical mechanics.
-Carroll, "Lecture notes on general relativity", http://arxiv.org/abs/gr-qc/9712019 -Wald, "General relativity" -Choquet-Bruhat et al., "Analysis, manifolds and physics" (for the differential geometry part) -Straumann, "General relativity (with applications to astrophysics)" -Weinberg, "Gravitation and Cosmology" -O'Neill, "Semi-Riemannian geometry (with applications to relativity)"