Comments: Blackboard lectures with detailed calculations. A list of exercises will be included.
Important: Previous registration is required. The number of places is constrained by the capacity of the room due to covid19 [16 places]. Basic background on general relativity, at the level of the Master course, is also necessary.
Organizer: Prof. J. Navarro-Salas
1. Gravitational collapse.
1.1 White dwarfs and the Chandrasekhar mass limit.
1.2 Neutron stars: need of GR.
1.3 Brief review: test particles and geodesics.
1.4 Brief review: symmetries and Killing vectors.
1.5 Oppenheimer-Snyder gravitational collapse.
2. Schwarzschild black hole solution.
2.0 Birchoff’s uniqueness theorem.
2.1 Eddington-Finkelstein coordinates: future and past event horizons.
2.2 Kruskal-Szekeres coordinates: eternal black holes.
2.3 Null hypersurfaces.
2.4 Event horizon vs apparent horizon.
2.5 Killing horizons and surface gravity.
2.6 Carter-Penrose diagrams. Conformal infinity.
3. Kerr black hole solution.
3.1 The Kerr-Newman solution. BH uniqueness theorems and no-Hair.
3.2 Principal null congruences and extension beyond event horizon.
3.3 Killing horizon and surface gravity.
3.4 Maximal extension of Kerr spacetime
3.6 Dragging of inertial frames and ergoregion.
3.7 Energy extraction: Penrose process and superradiance.
3.8 Predictability. Cauchy horizons.
3.9 Strong and weak cosmic censorship.