General Relativity

1 Unit · Graduate

First quarter: Review of special relativity and Newtonian gravity; Gravity as geometry of curved spacetime; Geodesics and conservation laws; Schwarzschild geometry; Tests of GR and the PPN formalism; Gravitational collapse and black holes; Rotating black holes and the Kerr geometry; Linearized gravity and gravitational waves; Cosmological models for the expanding Universe. Second quarter: Differential geometry, tensors, covariant derivatives; Riemann curvature and the field equation in vacuum; Energy-momentum tensor, the Einstein equation; Perturbation theory, gauge transformations; Emission of gravitational radiation; More advanced applications, as time permits, such as: relativistic stars, TOV equation and the Chandrasekhar limit, relativistic hydrodynamics; ADM formalism and numerical relativity; quantum mechanics in curved spacetime, inflationary cosmology.