I will start by explaining basic principles of General Relativity.
I will review the all familiar Einstein-vacuum space-times: Minkowski and
Schwarzschild, the latter giving the simplest example of a black hole
space-time, describe basic monotonicity property of the Einstein equations
and its use in the Penrose incompleteness theorem. I will then discuss the
evolution problem in General Relativity, explain how to construct rough
space-times and trapped surfaces, and explore several stability problems,
including that of black holes. In that context I will examine global
behavior of linear waves and explain the role of the celebrated red-shift effect.
November 12th, Wednesday, 5:00-6:00 pm
Tea will be served at 4:30pm