May 23rd – May 30th, 2024
Gran Sasso Science Institute, L'Aquila (IT)
Black holes are perhaps the most spectacular theoretical prediction of Einstein's theory of general relativity. Quite remarkably, the notion of black hole has a simple mathematical definition and already characterises the simplest non-trivial solution to the Einstein equations, the so-called Schwarzschild solution. The course will introduce the concept of a black hole and, in the case of the Schwarzschild solution, describe the influence of black holes on the propagation of waves. The latter aspect connects to fundamental questions concerning black holes, such as their stability as solutions to the Einstein equations.
Part I: General Relativity (4hrs)
Lecture 1: Basic Lorentzian geometry and causal structures
Lecture 2: The Einstein equations and the initial value formulation of General Relativity
Part II: Black holes (4hrs)
Lecture 3: Definition and basic properties of Schwarzschild black holes
Lecture 4: Ongoing research on black holes and open questions
Part III: Analysis of waves on Schwarzschild black holes (4hrs)
Lecture 5: Motivation and linear waves on Minkowski space
Lecture 6: Uniform boundedness of linear waves on the Schwarzschild exterior and outlook
Office hours: 3pm--4pm, PT-13 (Ex-INPS Building)
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