General Relativity and the Analysis of Black Hole Spacetimes - Einzelansicht

This course has two parts. The first part is an introduction to the theory of general relativity covering roughly the following topics:

(1) Introduction to Lorentzian geometry

(2) The geometry of the Schwarzschild and Kerr black hole solutions

(3) The initial value formulation of the Einstein Equations

(4) Penrose's singularity theorem

The second part will be devoted to the study of the wave equation on black hole spacetimes.

[1] S. Aretakis, "General Relativiy", Columbia Lecture Notes available from

https://www.math.toronto.edu/aretakis/General%20Relativity-Aretakis.pdf

[2] B. O'Neill , "Semi-Riemannian Geometry", Academic Press 

[3] R. Wald, "General Relativity", The University of Chicago Press

[4] H. Ringstroem, "The Cauchy Problem in General Relativity", EMS 

[5] M. Dafermos and I. Rodnianski, "Lectures on black holes and linear waves." 

In Evolution equations, Clay Mathematics Proceedings, Vol. 17, pages 97–205. Amer. Math. Soc.

Prerequisites: Familiarity with the concept of a manifold and some basic PDE theory for the second part will be useful but can also be obtained while attending the course.