Mathematical Relativity — 2nd Semester 2021/2022
AnnouncementsYou can see the final grades after the second exam on the side bar. Drop by my office if you want to take a look at your graded exam. SyllabusExamples: Minkowski space-time, Schwarzschild solution, Einstein, de Sitter, anti-de Sitter and Friedman-Lemaitre-Robertson-Walker universes; matching and Oppenheimer-Snyder collapse; Penrose diagrams. Causality: time orientabiliy, chronological and causal past and future, domain of dependence; chronological, stably causal and globally hyperbolic spacetimes. Singularities: Jacobi equation and conjugate points; energy conditions; existence of maximizing geodesics; Hawking and Penrose singularity theorems. Cauchy Problem: wave equation; Cauchy problems with constraints; Gauss-Coddazzi relations and 3+1 decomposition of the Einstein equation; Choquet-Bruhat theorem; constraint equations for the initial data. Positive Mass Theorem: Komar mass; Einstein-Hilbert action; Lagrangian and Hamiltonian formulation of the Einstein equations; ADM mass; positive mass theorem; Penrose inequality. Black Holes: Kerr solution; Killing horizons; surface gravity; Smarr formula; area theorem; black hole thermodynamics. BibliographyMain
Secundary
Grading PolicyHomework: Makes up 50% of the grade. Late homework will not be accepted. Final exam: Makes up 50% of the grade. Can be retaken if necessary. Homework
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