This course gives an introduction to Einstein's theory of general relativity. No prior knowledge of general relativity will be assumed, and an overview of the differential geometry needed to understand the field equations and spacetime geometries will be given. Beyond this, topics covered will include black holes and gravitational waves.
• Manifolds ◦ Gravity as geometry ◦ What is a manifold? ◦ Vectors again ◦ Tensors again ◦ The metric ◦ An expanding universe ◦ Causality ◦ Tensor densities
• Curvature ◦ Overview ◦ Covariant derivatives ◦ Parallel transport and geodesics ◦ Properties of geodesics ◦ The expanding universe revisited ◦ The Riemann curvature tensor ◦ Properties of the Riemann tensor ◦ Symmetries and Killing vectors ◦ Maximally symmetric spaces ◦ Geodesic deviation
• Gravitation ◦ Physics in curved spacetime ◦ Einstein’s equation ◦ Lagrangian formulation ◦ Properties of Einstein’s equation ◦ The cosmological constant ◦ Energy conditions ◦ The Equivalence Principle revisited ◦ Alternative theories
• The Schwarzschild Solution ◦ The Schwarzschild metric ◦ Birkhoff’s theorem ◦ Singularities ◦ Geodesics of Schwarzschild ◦ Experimental tests ◦ Schwarzschild black holes ◦ The maximally extended Schwarzschild solution ◦ Stars and black holes
• More General Black Holes ◦ The black hole zoo ◦ Event Horizons ◦ Killing Horizons ◦ Mass, charge, and spin ◦ Charged (Reissner-Nordström) black holes ◦ Rotating (Kerr) black holes ◦ The Penrose process and black-hole thermodynamics
• Perturbation Theory and Gravitational Radiation ◦ Linearized theory and gauge transformations ◦ Degrees of freedom ◦ Newtonian fields and photon trajectories ◦ Gravitational wave solutions ◦ Production of gravitational waves ◦ Energy loss due to gravitational radiation ◦ Detection of gravitational waves
NICOLA MAGGIORE (President)
NICODEMO MAGNOLI
PIERANTONIO ZANGHI'
GENERAL RELATIVITY (6 CFU)
