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.
The course is intended for a broad audience. No prior exposure to (special or) general relativity will be assumed. Knowledge of the basics of differential geometry (definition of smooth manifolds, vector fields, connections, curvature and geodesics) would be preferable, but not essential.
Chapters 1-4 of the textbook "General Relativity" (1984) by Wald is the suggested reference for a first read about general relativity (and include the preferable differential geometry background). The course will borrow material (and structure) from the "ETH Nachdiplom Lectures" (2013) by Dafermos. The "Clay Lectures" (2008) by Dafermos--Rodnianski are a more comprehensive presentation on the topic of the course. The most relevant journal reference for the course is "The redshift effect and radiation decay on black hole spacetimes" (2009) by Dafermos--Rodnianski.
Schedule:
May 23, 11am - 1pm, Room B;
May 24, 11am - 1pm, Room B;
May 27, 11am - 1pm, MLH;
May 28, 11am - 1pm, Room B;
May 29, 11am - 1pm, Room B;
May 30, 11am - 1pm, Room B.
For further information, please contact apde_aq@gssi.it
